4412:
19:
196:
68:
58:. Matrices have a long history of both study and application, leading to diverse ways of classifying matrices. A first group is matrices satisfying concrete conditions of the entries, including constant matrices. Important examples include the
314:
2445:
1343:
446:
The matrix of the linear map mapping the vector of the entries of a matrix to the vector of a part of the entries (for example the vector of the entries that are not below the main diagonal)
3810:
191:{\displaystyle I_{n}={\begin{bmatrix}1&0&\cdots &0\\0&1&\cdots &0\\\vdots &\vdots &\ddots &\vdots \\0&0&\cdots &1\end{bmatrix}}.}
1586:
1517:
1246:
3449:
1445:
229:
2283:
A square matrix, with dimensions a power of 2, the entries of which are +1 or −1, and the property that the dot product of any two distinct rows (or columns) is zero.
3862:
1471:
1540:
2224:
A matrix with all entries above the main diagonal equal to zero (lower triangular) or with all entries below the main diagonal equal to zero (upper triangular).
879:
A square matrix with entries 0, 1 and −1 such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign.
237:
3917:— a matrix representing the variance of the partial derivative, with respect to a parameter, of the log of the likelihood function of a random variable.
4116:
4352:
3851:— a matrix which, when multiplied with a vector, has the same effect as subtracting the mean of the components of the vector from every component.
3455:
3155:
A matrix whose eigenvalues have strictly negative real part. A stable system of differential equations may be represented by a
Hurwitz matrix.
4517:
1894:
A block-hierarchical matrix. It consist of growing blocks placed along the diagonal, each block is itself a Parisi matrix of a smaller size.
4148:
344:
The list below comprises matrices whose elements are constant for any given dimension (size) of matrix. The matrix entries will be denoted
3107:
1867:
Synonym for kernel-Hermitian matrices. Examples include (but not limited) to
Hermitian, skew-Hermitian matrices, and normal matrices.
4535:
4069:— a matrix equal to the degree matrix minus the adjacency matrix for a graph, used to find the number of spanning trees in the graph.
4182:
2352:
1832:
Synonym for kernel-symmetric matrices. Examples include (but not limited to) symmetric, skew-symmetric, and normal matrices.
1749:
1595:
1877:
A matrix partitioned into sub-matrices, or equivalently, a matrix whose entries are themselves matrices rather than scalars.
3551:
3516:
2998:
1266:
3929:— doubly stochastic matrix whose entries are the squares of the absolute values of the entries of some orthogonal matrix
3073:
3980:— a doubly stochastic matrix whose entries are the squares of the absolute values of the entries of some unitary matrix
3572:
2654:
2631:
452:
434:
412:
1160:
A square matrix with zero diagonal and +1 and −1 off the diagonal, such that CC is a multiple of the identity matrix.
1907:
A matrix with the only nonzero entries on the main diagonal and the two diagonals just above and below the main one.
1661:
An "almost" triangular matrix, for example, an upper
Hessenberg matrix has zero entries below the first subdiagonal.
4204:
3525:
2719:
2136:
Sparse matrix algorithms can tackle huge sparse matrices that are utterly impractical for dense matrix algorithms.
1409:
A square matrix in the form of an identity matrix but with arbitrary entries in one column below the main diagonal.
1258:
2606:
3914:
3705:
3426:
3418:
3379:
3352:
2985:
2236:
A matrix with the only nonzero entries on the main diagonal and the diagonals just above and below the main one.
4158:
3900:
3724:
3531:
3394:
3174:
1032:
3741:
4258:
4162:
4072:
2203:
1841:
1806:
1167:
874:
4082:
1397:
A matrix that can be derived from another matrix through a sequence of elementary row or column operations.
328:
of the matrix with other matrices. Finally, many domains, both in mathematics and other sciences including
4325:— an 'almost' diagonalised matrix, where the only non-zero elements appear on the lead and superdiagonals.
4142:
3926:
3356:
3337:
2535:
2290:
1717:
1100:
1037:
A block matrix which is essentially a tridiagonal matrix but with submatrices in place of scalar elements.
935:
A square matrix containing zeros in all entries except for the first row, first column, and main diagonal.
4322:
4190:
4056:
4040:
3720:
3714:
3125:
3091:
2875:
2306:
A number of matrix-related notions is about properties of products or inverses of the given matrix. The
2247:
2092:
2068:
1004:
914:
898:
673:
4411:
3733:
3101:
3838:
1545:
4375:
4346:
4292:
4172:
3977:
3655:
3642:
3142:
2691:
2531:
1902:
886:
634:
47:
27:
799:
The following lists matrices whose entries are subject to certain conditions. Many of them apply to
4328:
4264:
4138:
4060:
3621:
3497:
3333:
2967:
2795:
2750:
2467:
2074:
2056:
2001:
1930:
1889:
1845:
1638:
1476:
3378:
A matrix having the coefficients of a polynomial as last column, and having the polynomial as its
1203:
658:
identity matrix, they form an orthogonal basis for the 2 × 2 complex
Hermitian matrices.
4417:
4342:
4336:
4196:
4178:
4022:
3958:
3854:
3831:
3672:
3512:
3312:
2995:
2849:
2254:
2231:
1914:
1790:
992:
494:
441:
419:
397:
997:
A square matrix that is symmetric with respect to its main diagonal and its main cross-diagonal.
681:
1424:
208:
18:
4540:
4513:
4332:
4252:
4246:
4236:
4228:
4200:
3964:
3950:
3903:— a non-negative matrix such that each row and each column sums to 1 (thus the matrix is both
3890:
3872:
3699:
3664:
3316:
3060:
2991:
2917:
2820:
2699:
2662:
2626:
2558:
2219:
1973:
1656:
1392:
1380:
1191:
1155:
958:
651:
A set of three 2 × 2 complex
Hermitian and unitary matrices. When combined with the
963:
A matrix with elements only on the main diagonal and either the superdiagonal or subdiagonal.
4367:
4286:
4255:- a matrix in Microwave Engineering that describes how the power move in a multiport system.
4214:
4210:
4134:
4120:
4086:
4076:
4066:
4052:
4026:
4001:
3932:
3848:
3679:
3593:
3464:
3432:
3413:
3373:
3322:
The composition of two functions can be expressed as the product of their
Carleman matrices
3299:
3282:
3265:
3202:
3186:
3081:
2934:
2879:
2865:
2841:
2812:
2764:
2715:
2141:
2044:
1632:
1404:
1143:
930:
862:
677:
667:
599:
425:
2651:
The name projection matrix inspires from the observation of projection of a point multiple
542:
A square diagonal matrix, with all entries on the main diagonal equal to 1, and the rest 0.
4454:
4152:
4030:
3866:
3615:
3545:
3442:
3436:
3407:
3366:
3346:
3306:
3248:
3239:
3012:
3002:
2953:
2905:
2191:
2023:
1989:
1607:
1352:
1179:
1050:
596:
537:
459:
352:
59:
1450:
867:
A matrix in which successive columns have a particular function applied to their entries.
1522:
309:{\displaystyle O_{2\times 3}={\begin{pmatrix}0&0&0\\0&0&0\end{pmatrix}}}
4478:
4402:
4361:
4282:
4268:
4224:
4220:
4168:
4130:
4046:
3994:
3630:
3506:
3487:
3388:
3274:
3254:
3194:
3150:
3131:
2961:
2923:
2897:
2668:
2307:
2116:
1737:
1692:
1680:
1385:
A square matrix derived by applying an elementary row operation to the identity matrix.
1044:
971:
841:
646:
607:
502:
325:
1923:, a square matrix with exactly one 1 in each row and column, and all other elements 0.
4529:
4505:
4357:
4309:
4036:
3968:
3579:
3560:
3493:
3470:
3398:
3327:
2789:
2128:
2017:
1725:
1668:
1619:
1358:
1172:
A matrix with all rows and columns mutually orthogonal, whose entries are unimodular.
1060:
804:
628:
563:
529:
465:
3639:, primarily for the algebraic analysis of topological properties of knots and links.
1184:
A matrix whose entries are generated by the determinants of all minors of a matrix.
4232:
4103:
3990:
3972:
3954:
3649:
3115:
3087:
2278:
1872:
1766:
1020:
1010:
724:
1730:
A matrix of non-negative real numbers, such that the entries in each row sum to 1.
811:
joining the upper left corner and the lower right one or equivalently the entries
3923:— a square matrix used in statistics to relate fitted values to observed values.
3842:
3685:
3636:
3603:
3585:
3478:
3474:
3288:
3258:
3207:
A real symmetric positive definite matrix with nonpositive off-diagonal entries.
3066:
2855:
2455:
2209:
2032:
1920:
942:
772:
202:
39:
31:
4384:— the determinant of a matrix of functions and their derivatives such that row
4055:— a matrix representing a relationship between two classes of objects (usually
2466:. A number of notions are concerned with the failure of this commutativity. An
4407:
4272:
3920:
3880:
3827:
3568:
3535:
3138:
2007:
1979:
1416:
1368:
403:
321:
2061:
A matrix where a single element is one and the rest of the elements are zero.
424:
The matrix of the linear map mapping the vector of the distinct entries of a
4381:
4296:
4186:
3589:
3362:
3292:
3244:
2826:
2599:
2147:
2121:
A rearrangement of the entries of a banded matrix which requires less space.
2098:
1810:
729:
A matrix with ones on the superdiagonal or subdiagonal and zeroes elsewhere.
333:
3690:
The
Sylvester matrix is nonsingular if and only if the two polynomials are
1624:
A matrix with constant skew-diagonals; also an upside down
Toeplitz matrix.
1600:
A square matrix with precisely one nonzero element in each row and column.
4242:
3211:
3162:
2871:
2729:
1935:
A matrix that is symmetric about its northeast–southwest diagonal, i.e.,
808:
4106:— a generalization of the Edmonds matrix for a balanced bipartite graph.
4079:
but with −1 for adjacency; +1 for nonadjacency; 0 on the diagonal.
3270:
Matrix whose rows are concatenations of the rows of two smaller matrices
3691:
3669:
A matrix of scores which express the similarity between two data points
1754:
A square matrix with exactly one non-zero entry in each row and column.
1612:
A square matrix with entries +1, −1 whose rows are mutually orthogonal.
329:
35:
4510:
Handbook of Linear
Algebra (Discrete Mathematics and Its Applications)
3608:
A matrix that occurs in the study of analytical interpolation problems
891:
A square matrix with all entries off the anti-diagonal equal to zero.
803:
only, that is matrices with the same number of columns and rows. The
51:
4249:
that connects asymptotic (infinite past and future) particle states.
2540:
A matrix whose inverse is equal to its entrywise complex conjugate:
824:. The other diagonal is called anti-diagonal (or counter-diagonal).
336:, have particular matrices that are applied chiefly in these areas.
4299:, representing a molecule in terms of its relative atomic geometry.
4335:
are linearly independent if there is no way to construct one from
2049:
A diagonal matrix where the diagonal elements are either +1 or −1.
947:
A square matrix whose non-zero entries are confined to a diagonal
17:
4133:— a matrix describing the statistical state of a quantum system.
3114:. Equivalently, at least one of its eigenvalues has at least two
2734:
A matrix that preserves distances, i.e., a matrix that satisfies
2653:
times onto a subspace(plane or a line) giving the same result as
1673:
A square matrix whose main diagonal comprises only zero elements.
3684:
A square matrix whose entries come from the coefficients of two
22:
Several important classes of matrices are subsets of each other.
3412:
The square matrix formed by the pairwise distances of a set of
1148:
A matrix where each row is a circular shift of its predecessor.
4276:
4100:
matches or opposes that of an initially specified orientation.
2724:
to reflect a point about a plane or line) have this property.
1373:
Multiplying by a vector gives the DFT of the vector as result.
46:(plural matrices, or less commonly matrixes) is a rectangular
3167:
A Z-matrix with eigenvalues whose real parts are nonnegative.
1897:
In theory of spin-glasses is also known as a replica matrix.
767:
Multiplication by it shifts matrix elements by one position.
320:
Further ways of classifying matrices are according to their
1093:) injective sequences (i.e., taking every value only once).
468:
with ones on the anti-diagonal, and zeroes everywhere else.
3812:, used for rank-reduction & biconjugate decompositions
2990:
A matrix for which every non-singular square submatrix is
3841:— a square matrix with entries +1, −1, with equal
2454:. Unlike the product of numbers, matrix products are not
2440:{\displaystyle (C)_{i,j}=\sum _{r=1}^{n}A_{i,r}B_{r,j}.}
4185:; these matrices are one notable representation of the
3431:
A matrix that describes the pairwise distances between
3086:
A square matrix that does not have a complete basis of
3042:
Matrices with conditions on eigenvalues or eigenvectors
2295:
A matrix with all off-diagonal entries less than zero.
2246:
A generalization to three dimensions of the concept of
4370:— a matrix in this form is the result of applying the
3989:
The following matrices find their main application in
3971:
of conditions changing from one state to another in a
3826:
The following matrices find their main application in
3454:
The matrix formed from the fundamental solutions of a
2073:
A square matrix which is equal to the negative of its
265:
90:
4479:"Non-derogatory matrix - Encyclopedia of Mathematics"
3744:
3332:
A matrix associated with either a finite-dimensional
3065:
A square matrix whose successive powers approach the
2355:
1742:
A matrix whose off-diagonal entries are non-negative.
1548:
1525:
1479:
1453:
1427:
1269:
1206:
240:
211:
71:
4217:
which has a varying number of elements in each row.
4155:
that relates corresponding points in stereo images.
3393:A matrix which describes the relations between the
2922:
An invertible matrix with entries in the integers (
2571:are congruent if there exists an invertible matrix
1338:{\displaystyle |a_{ii}|>\sum _{j\neq i}|a_{ij}|}
1025:
A matrix partitioned in sub-matrices called blocks.
4199:— a matrix used in a variety of fields, including
3804:
3179:A Hermitian matrix with every eigenvalue positive.
2439:
1580:
1534:
1511:
1465:
1439:
1337:
1240:
308:
223:
190:
4312:, a matrix used as an example for test purposes.
4039:— a diagonal matrix defining the degree of each
3883:of several random variables. Sometimes called a
2939:A square matrix with all eigenvalues equal to 1.
2704:A square matrix which is its own inverse, i.e.,
4231:to describe the inter-relationship of a set of
4096:is 1 or −1, accordingly as the direction
2929:Necessarily the determinant is +1 or −1.
2271:, etc., and each row uses a different variable.
2133:A matrix with relatively few non-zero elements.
2097:A matrix which is equal to the negative of its
2037:A matrix whose entries are either +1, 0, or −1.
1783:, etc., and each row uses a different variable.
4261:— exponent of state matrix in control systems.
2966:A square matrix whose inverse is equal to its
4004:— a square matrix representing a graph, with
1357:A square matrix with all entries outside the
976:A matrix whose entries are all either 0 or 1.
26:This article lists some important classes of
8:
3017:A square matrix the entries of which are in
1248:is nonnegative for every nonnegative vector
966:Sometimes defined differently, see article.
3550:The matrix of the partial derivatives of a
2502:is uniquely determined, and is also called
2498:. An inverse need not exist. If it exists,
1105:A matrix symmetric about its center; i.e.,
1065:A matrix whose elements are of the form 1/(
4317:Other matrix-related terms and definitions
3224:
3045:
2516:
826:
680:; entires of the inverse are given by the
428:to the vector of all entries of the matrix
379:
3793:
3774:
3758:
3743:
2422:
2406:
2396:
2385:
2366:
2354:
1566:
1553:
1547:
1524:
1500:
1487:
1478:
1452:
1426:
1330:
1321:
1312:
1300:
1288:
1279:
1270:
1268:
1226:
1205:
846:A matrix with all elements either 0 or 1.
260:
245:
239:
210:
85:
76:
70:
4111:Matrices used in science and engineering
3961:. The sum of entries of any row is one.
3805:{\displaystyle A-(y^{T}Ax)^{-1}Axy^{T}A}
3355:of a square matrix, that is, the signed
2882:. Equivalently, a matrix that satisfies
2667:A square matrix having a multiplicative
1697:A matrix with all entries either 0 or 1.
1685:A matrix whose entries are all integers.
1049:A matrix whose entries are taken from a
777:A matrix with all entries equal to zero.
4429:
4353:Matrix representation of conic sections
4049:— a square matrix of a bipartite graph.
3456:system of linear differential equations
2910:A square matrix that is not invertible.
2825:A matrix whose inverse is equal to its
2794:A square matrix that commutes with its
2605:A square matrix that commutes with its
2212:of all its square submatrices positive.
612:A matrix with all entries equal to one.
4512:, Boca Raton: Chapman & Hall/CRC,
4437:
3257:is its adjugate matrix divided by its
2478:(necessarily of the same dimension as
2146:A square matrix which is equal to its
1795:A matrix with all nonnegative entries.
1637:A square matrix which is equal to its
4165:, used in machine learning processes.
3492:The symmetric matrix of the pairwise
2994:. This has some implications in the
2780:Equivalently, the only eigenvalue of
2722:(Also known as 'reflection matrices'
1840:A square matrix whose null space (or
1805:A square matrix whose null space (or
1627:A square Hankel matrix is symmetric.
7:
4448:
4446:
4271:, which describes mutation rates of
4183:generalization of the Pauli matrices
4149:Fundamental matrix (computer vision)
633:A matrix containing the entries of
3592:, that represents the payoffs in a
3221:Matrices generated by specific data
2811:They are the matrices to which the
1994:A matrix with all positive entries.
1473:having the greatest common divisor
406:that maps a matrix to its transpose
389:Symbolic description of the entries
324:, or by imposing conditions on the
4374:procedure to a matrix (as used in
3815:Analysis of matrix decompositions
2302:Matrices satisfying some equations
1200:with real coefficients, such that
1013:with entries only on the diagonal.
676:. Matrix entries are given by the
14:
3596:where players move simultaneously
2196:A matrix with constant diagonals.
1369:Discrete Fourier-transform matrix
4410:
4117:Cabibbo–Kobayashi–Maskawa matrix
4075:— a matrix similar to the usual
4063:in the context of graph theory).
3939:matrix, formed by inverting the
1581:{\displaystyle x_{i},x_{j}\in S}
3879:matrix, formed by the pairwise
3861:matrix, formed by the pairwise
2636:A matrix that has the property
2594:Compare with similar matrices.
2553:Compare with unitary matrices.
2450:This matrix product is denoted
1263:A matrix whose entries satisfy
3771:
3751:
3076:have magnitude less than one.
2773:= 0 for some positive integer
2363:
2356:
1759:generalized permutation matrix
1596:Generalized permutation matrix
1506:
1480:
1460:
1454:
1331:
1313:
1289:
1271:
1216:
1210:
1:
3985:Matrices used in graph theory
3552:function of several variables
3517:function of several variables
3273:Used for performing the same
3141:, that is, a complete set of
2690:Invertible matrices form the
1919:A matrix representation of a
1712:. Can be used to represent a
1512:{\displaystyle (x_{i},x_{j})}
795:Specific patterns for entries
4123:to describe the strength of
4029:that describes adjacency in
3967:— a matrix representing the
2896:Equivalently, a matrix with
1241:{\displaystyle f(x)=x^{T}Ax}
4119:— a unitary matrix used in
3822:Matrices used in statistics
3573:Sum-of-squares optimization
2854:A matrix whose columns are
2769:A square matrix satisfying
2022:A matrix whose entries are
2006:A matrix whose entries are
1978:A matrix whose entries are
351:. The table below uses the
4557:
4392:−1) derivative of row one.
4360:— a generalization of the
4285:— a square matrix used in
4205:linear-quadratic regulator
3538:passing through the origin
3513:second partial derivatives
3496:of a set of vectors in an
3029:for some positive integer
2866:Partially Isometric matrix
2602:or Range-Hermitian matrix
1259:Diagonally dominant matrix
807:of a square matrix is the
4536:Mathematics-related lists
3915:Fisher information matrix
3706:symplectic transformation
3427:Euclidean distance matrix
3419:Euclidean distance matrix
3380:characteristic polynomial
2986:Totally unimodular matrix
1440:{\displaystyle n\times n}
224:{\displaystyle m\times n}
4187:infinitesimal generators
4159:Fuzzy associative matrix
3901:Doubly stochastic matrix
3863:correlation coefficients
3725:geometric transformation
3620:A matrix representing a
3175:Positive-definite matrix
2900:that are either 0 or 1.
1033:Block tridiagonal matrix
4455:"Matrix Multiplication"
4259:State transition matrix
4163:artificial intelligence
4089:in which each non-zero
4073:Seidel adjacency matrix
3311:Infinite matrix of the
2952:is nilpotent. See also
2204:Totally positive matrix
1168:Complex Hadamard matrix
875:Alternating sign matrix
4483:encyclopediaofmath.org
3927:Orthostochastic matrix
3806:
3473:, a matrix whose rows
3338:semisimple Lie algebra
3319:and its integer powers
3110:is of order less than
3106:A square matrix whose
2441:
2401:
1837:Null-Hermitian matrix
1802:Null-symmetric matrix
1582:
1536:
1513:
1467:
1441:
1339:
1242:
1101:Centrosymmetric matrix
310:
225:
192:
23:
4459:mathworld.wolfram.com
4323:Jordan canonical form
4191:special unitary group
4083:Skew-adjacency matrix
4025:— a special class of
3893:— another name for a
3807:
3738:A matrix of the form
3721:linear transformation
3715:Transformation matrix
3704:The real matrix of a
3511:The square matrix of
3134:to a diagonal matrix.
3126:Diagonalizable matrix
2876:orthogonal complement
2607:Moore–Penrose inverse
2462:need not be equal to
2442:
2381:
2259:A row consists of 1,
2248:two-dimensional array
2093:Skew-symmetric matrix
2069:Skew-Hermitian matrix
1583:
1537:
1514:
1468:
1442:
1340:
1243:
1005:Block-diagonal matrix
923:skew-symmetric matrix
915:Anti-symmetric matrix
907:skew-Hermitian matrix
899:Anti-Hermitian matrix
674:Dirichlet convolution
668:Redheffer matrix
311:
226:
193:
21:
4376:Gaussian elimination
4173:quantum field theory
4171:— 4 × 4 matrices in
4151:— a 3 × 3 matrix in
3978:Unistochastic matrix
3957:matrix describing a
3742:
3656:shear transformation
3643:Alexander polynomial
3287:Square matrix whose
3143:linearly independent
2870:A matrix that is an
2720:Householder matrices
2692:general linear group
2671:, that is, a matrix
2536:Coninvolutory matrix
2353:
1903:Pentadiagonal matrix
1546:
1523:
1477:
1451:
1425:
1267:
1204:
887:Anti-diagonal matrix
460:Exchange matrix
238:
209:
69:
4453:Weisstein, Eric W.
4372:forward elimination
4337:linear combinations
4329:Linear independence
4265:Substitution matrix
4213:— a matrix used in
4011:non-zero if vertex
3498:inner product space
3334:associative algebra
3313:Taylor coefficients
3255:inverse of a matrix
3210:Special case of an
2968:conjugate transpose
2796:conjugate transpose
2751:conjugate transpose
2075:conjugate transpose
2057:Single-entry matrix
2002:Quaternionic matrix
1931:Persymmetric matrix
1846:conjugate transpose
1639:conjugate transpose
1466:{\displaystyle (S)}
4418:Mathematics portal
4347:exponential series
4343:Matrix exponential
4197:Hamiltonian matrix
4179:Gell-Mann matrices
4023:Biadjacency matrix
3959:stochastic process
3945:information matrix
3943:. Also called the
3855:Correlation matrix
3832:probability theory
3802:
3673:Sequence alignment
3534:with respect to a
3526:Householder matrix
3450:Fundamental matrix
3421:is a special case
3295:of two polynomials
3108:minimal polynomial
3090:, and is thus not
2996:linear programming
2850:Orthonormal matrix
2716:Signature matrices
2437:
2255:Vandermonde matrix
2232:Tridiagonal matrix
1915:Permutation matrix
1873:Partitioned matrix
1844:) is equal to its
1809:) is equal to its
1791:Nonnegative matrix
1771:A row consists of
1578:
1535:{\displaystyle ij}
1532:
1509:
1463:
1437:
1335:
1311:
1238:
993:Bisymmetric matrix
836:Notes, references
495:permutation matrix
442:Elimination matrix
420:Duplication matrix
402:The matrix of the
398:Commutation matrix
306:
300:
221:
188:
179:
24:
4519:978-1-58488-510-8
4440:, Ch. 31.3.
4345:— defined by the
4304:Specific matrices
4253:Scattering matrix
4247:quantum mechanics
4229:quantum chemistry
4201:quantum mechanics
3965:Transition matrix
3951:Stochastic matrix
3941:covariance matrix
3895:covariance matrix
3891:Dispersion matrix
3885:dispersion matrix
3873:Covariance matrix
3819:
3818:
3734:Wedderburn matrix
3700:Symplectic matrix
3665:Similarity matrix
3317:analytic function
3218:
3217:
3102:Derogatory matrix
3061:Convergent matrix
3039:
3038:
2918:Unimodular matrix
2821:Orthogonal matrix
2700:Involutory matrix
2663:Invertible matrix
2632:Projection Matrix
2627:Idempotent matrix
2470:of square matrix
2458:, that is to say
2299:
2298:
2220:Triangular matrix
1974:Polynomial matrix
1657:Hessenberg matrix
1393:Equivalent matrix
1381:Elementary matrix
1296:
1192:Copositive matrix
1156:Conference matrix
959:Bidiagonal matrix
792:
791:
719:A (0, 1)-matrix.
635:Pascal's triangle
361:for two integers
340:Constant matrices
4548:
4522:
4493:
4492:
4490:
4489:
4475:
4469:
4468:
4466:
4465:
4450:
4441:
4434:
4420:
4415:
4414:
4368:Row echelon form
4287:computer science
4267:— a matrix from
4215:computer science
4211:Irregular matrix
4125:flavour-changing
4121:particle physics
4087:adjacency matrix
4077:adjacency matrix
4067:Laplacian matrix
4053:Incidence matrix
4031:bipartite graphs
4027:adjacency matrix
4002:Adjacency matrix
3933:Precision matrix
3909:right stochastic
3867:random variables
3849:Centering matrix
3839:Bernoulli matrix
3811:
3809:
3808:
3803:
3798:
3797:
3782:
3781:
3763:
3762:
3719:The matrix of a
3680:Sylvester matrix
3654:The matrix of a
3594:normal form game
3530:The matrix of a
3465:Generator matrix
3397:that generate a
3374:Companion matrix
3300:Sylvester matrix
3277:on two matrices
3266:Augmented matrix
3225:
3203:Stieltjes matrix
3187:Stability matrix
3130:A square matrix
3082:Defective matrix
3046:
3020:
3019:{0, 1, −1}
2951:
2935:Unipotent matrix
2842:orthogonal group
2813:spectral theorem
2765:Nilpotent matrix
2730:Isometric matrix
2586:
2559:Congruent matrix
2549:
2517:
2490:. Equivalently,
2446:
2444:
2443:
2438:
2433:
2432:
2417:
2416:
2400:
2395:
2377:
2376:
2142:Symmetric matrix
2045:Signature matrix
2024:random variables
1633:Hermitian matrix
1587:
1585:
1584:
1579:
1571:
1570:
1558:
1557:
1541:
1539:
1538:
1533:
1518:
1516:
1515:
1510:
1505:
1504:
1492:
1491:
1472:
1470:
1469:
1464:
1446:
1444:
1443:
1438:
1405:Frobenius matrix
1344:
1342:
1341:
1336:
1334:
1329:
1328:
1316:
1310:
1292:
1287:
1286:
1274:
1247:
1245:
1244:
1239:
1231:
1230:
1196:A square matrix
1144:Circulant matrix
931:Arrowhead matrix
863:Alternant matrix
827:
707:= 1; otherwise,
678:divisor function
600:symmetric matrix
525: − 1).
426:symmetric matrix
380:
315:
313:
312:
307:
305:
304:
256:
255:
230:
228:
227:
222:
197:
195:
194:
189:
184:
183:
81:
80:
4556:
4555:
4551:
4550:
4549:
4547:
4546:
4545:
4526:
4525:
4520:
4504:
4501:
4496:
4487:
4485:
4477:
4476:
4472:
4463:
4461:
4452:
4451:
4444:
4435:
4431:
4427:
4416:
4409:
4399:
4319:
4306:
4153:computer vision
4113:
4094:
4009:
3987:
3905:left stochastic
3824:
3789:
3770:
3754:
3740:
3739:
3616:Rotation matrix
3546:Jacobian matrix
3443:distance matrix
3437:Euclidean space
3408:Distance matrix
3367:Adjugate matrix
3359:, of the matrix
3347:Cofactor matrix
3307:Carleman matrix
3249:cofactor matrix
3240:Adjugate matrix
3223:
3044:
3018:
3013:Weighing matrix
3003:integer program
2954:unipotent group
2943:
2906:Singular matrix
2898:singular values
2723:
2652:
2630:
2576:
2545:
2532:Circular matrix
2418:
2402:
2362:
2351:
2350:
2304:
2192:Toeplitz matrix
2183:
2170:
1990:Positive matrix
1965:
1943:
1750:Monomial matrix
1608:Hadamard matrix
1562:
1549:
1544:
1543:
1521:
1520:
1496:
1483:
1475:
1474:
1449:
1448:
1423:
1422:
1353:Diagonal matrix
1317:
1275:
1265:
1264:
1222:
1202:
1201:
1180:Compound matrix
1135:
1113:
1091:
1084:
1077:
1070:
1051:Boolean algebra
823:
801:square matrices
797:
784:
764:
753:
747:
736:
715:
694:
682:Möbius function
657:
619:
574:
556:
549:
538:Identity matrix
516:
490:
475:
360:
353:Kronecker delta
349:
342:
299:
298:
293:
288:
282:
281:
276:
271:
261:
241:
236:
235:
231:. For example:
207:
206:
178:
177:
172:
167:
162:
156:
155:
150:
145:
140:
134:
133:
128:
123:
118:
112:
111:
106:
101:
96:
86:
72:
67:
66:
60:identity matrix
12:
11:
5:
4554:
4552:
4544:
4543:
4538:
4528:
4527:
4524:
4523:
4518:
4506:Hogben, Leslie
4500:
4497:
4495:
4494:
4470:
4442:
4428:
4426:
4423:
4422:
4421:
4406:
4405:
4403:Perfect matrix
4398:
4395:
4394:
4393:
4379:
4365:
4362:inverse matrix
4355:
4350:
4340:
4339:of the others.
4331:— two or more
4326:
4318:
4315:
4314:
4313:
4305:
4302:
4301:
4300:
4295:— a matrix in
4290:
4283:Supnick matrix
4280:
4269:bioinformatics
4262:
4256:
4250:
4245:— a matrix in
4240:
4225:Gramian matrix
4221:Overlap matrix
4218:
4208:
4207:(LQR) systems.
4194:
4176:
4169:Gamma matrices
4166:
4161:— a matrix in
4156:
4146:
4131:Density matrix
4128:
4112:
4109:
4108:
4107:
4101:
4092:
4080:
4070:
4064:
4050:
4047:Edmonds matrix
4044:
4034:
4020:
4007:
3995:network theory
3986:
3983:
3982:
3981:
3975:
3962:
3948:
3935:— a symmetric
3930:
3924:
3918:
3912:
3898:
3888:
3875:— a symmetric
3870:
3857:— a symmetric
3852:
3846:
3823:
3820:
3817:
3816:
3813:
3801:
3796:
3792:
3788:
3785:
3780:
3777:
3773:
3769:
3766:
3761:
3757:
3753:
3750:
3747:
3736:
3730:
3729:
3727:
3717:
3711:
3710:
3708:
3702:
3696:
3695:
3694:to each other
3688:
3682:
3676:
3675:
3670:
3667:
3661:
3660:
3658:
3652:
3646:
3645:
3640:
3633:
3631:Seifert matrix
3627:
3626:
3624:
3618:
3612:
3611:
3609:
3606:
3600:
3599:
3597:
3582:
3576:
3575:
3565:
3563:
3557:
3556:
3554:
3548:
3542:
3541:
3539:
3528:
3522:
3521:
3519:
3509:
3507:Hessian matrix
3503:
3502:
3500:
3494:inner products
3490:
3488:Gramian matrix
3484:
3483:
3481:
3467:
3461:
3460:
3458:
3452:
3446:
3445:
3439:
3429:
3423:
3422:
3416:
3410:
3404:
3403:
3401:
3391:
3389:Coxeter matrix
3385:
3384:
3382:
3376:
3370:
3369:
3360:
3351:Formed by the
3349:
3343:
3342:
3340:
3330:
3324:
3323:
3320:
3309:
3303:
3302:
3296:
3285:
3279:
3278:
3275:row operations
3271:
3268:
3262:
3261:
3251:
3242:
3236:
3235:
3232:
3229:
3222:
3219:
3216:
3215:
3208:
3205:
3199:
3198:
3195:Hurwitz matrix
3191:
3189:
3183:
3182:
3180:
3177:
3171:
3170:
3168:
3165:
3159:
3158:
3156:
3153:
3151:Hurwitz matrix
3147:
3146:
3145:eigenvectors.
3135:
3128:
3122:
3121:
3119:
3104:
3098:
3097:
3095:
3092:diagonalizable
3084:
3078:
3077:
3070:
3063:
3057:
3056:
3053:
3050:
3043:
3040:
3037:
3036:
3034:
3015:
3009:
3008:
3006:
2988:
2982:
2981:
2979:
2964:
2962:Unitary matrix
2958:
2957:
2942:Equivalently,
2940:
2937:
2931:
2930:
2927:
2924:integer matrix
2920:
2914:
2913:
2911:
2908:
2902:
2901:
2894:
2868:
2862:
2861:
2859:
2852:
2846:
2845:
2840:They form the
2838:
2823:
2817:
2816:
2809:
2792:
2786:
2785:
2778:
2767:
2761:
2760:
2758:
2732:
2726:
2725:
2713:
2702:
2696:
2695:
2688:
2665:
2659:
2658:
2655:one projection
2649:
2634:
2623:
2622:
2620:
2603:
2596:
2595:
2592:
2561:
2555:
2554:
2551:
2538:
2528:
2527:
2524:
2521:
2448:
2447:
2436:
2431:
2428:
2425:
2421:
2415:
2412:
2409:
2405:
2399:
2394:
2391:
2388:
2384:
2380:
2375:
2372:
2369:
2365:
2361:
2358:
2308:matrix product
2303:
2300:
2297:
2296:
2293:
2287:
2286:
2284:
2281:
2275:
2274:
2272:
2257:
2251:
2250:
2244:
2240:
2239:
2237:
2234:
2228:
2227:
2225:
2222:
2216:
2215:
2213:
2208:A matrix with
2206:
2200:
2199:
2197:
2194:
2188:
2187:
2185:
2175:
2162:
2144:
2138:
2137:
2134:
2131:
2125:
2124:
2122:
2119:
2117:Skyline matrix
2113:
2112:
2110:
2095:
2089:
2088:
2086:
2071:
2065:
2064:
2062:
2059:
2053:
2052:
2050:
2047:
2041:
2040:
2038:
2035:
2029:
2028:
2026:
2020:
2014:
2013:
2011:
2004:
1998:
1997:
1995:
1992:
1986:
1985:
1983:
1976:
1970:
1969:
1967:
1948:
1939:
1933:
1927:
1926:
1924:
1917:
1911:
1910:
1908:
1905:
1899:
1898:
1895:
1892:
1886:
1885:
1878:
1875:
1869:
1868:
1865:
1838:
1834:
1833:
1830:
1803:
1799:
1798:
1796:
1793:
1787:
1786:
1784:
1769:
1763:
1762:
1755:
1752:
1746:
1745:
1743:
1740:
1738:Metzler matrix
1734:
1733:
1731:
1728:
1722:
1721:
1710:Boolean matrix
1698:
1695:
1693:Logical matrix
1689:
1688:
1686:
1683:
1681:Integer matrix
1677:
1676:
1674:
1671:
1665:
1664:
1662:
1659:
1653:
1652:
1650:
1635:
1629:
1628:
1625:
1622:
1616:
1615:
1613:
1610:
1604:
1603:
1601:
1598:
1592:
1591:
1589:
1577:
1574:
1569:
1565:
1561:
1556:
1552:
1531:
1528:
1508:
1503:
1499:
1495:
1490:
1486:
1482:
1462:
1459:
1456:
1436:
1433:
1430:
1419:
1413:
1412:
1410:
1407:
1401:
1400:
1398:
1395:
1389:
1388:
1386:
1383:
1377:
1376:
1374:
1371:
1365:
1364:
1362:
1361:equal to zero.
1355:
1349:
1348:
1346:
1333:
1327:
1324:
1320:
1315:
1309:
1306:
1303:
1299:
1295:
1291:
1285:
1282:
1278:
1273:
1261:
1255:
1254:
1252:
1237:
1234:
1229:
1225:
1221:
1218:
1215:
1212:
1209:
1194:
1188:
1187:
1185:
1182:
1176:
1175:
1173:
1170:
1164:
1163:
1161:
1158:
1152:
1151:
1149:
1146:
1140:
1139:
1137:
1118:
1109:
1103:
1097:
1096:
1094:
1089:
1082:
1075:
1068:
1063:
1057:
1056:
1054:
1047:
1045:Boolean matrix
1041:
1040:
1038:
1035:
1029:
1028:
1026:
1023:
1017:
1016:
1014:
1007:
1001:
1000:
998:
995:
989:
988:
985:logical matrix
977:
974:
968:
967:
964:
961:
955:
954:
952:
945:
939:
938:
936:
933:
927:
926:
919:
917:
911:
910:
903:
901:
895:
894:
892:
889:
883:
882:
880:
877:
871:
870:
868:
865:
859:
858:
855:logical matrix
847:
844:
838:
837:
834:
831:
815:
796:
793:
790:
789:
787:
782:
778:
775:
769:
768:
765:
756:
751:
739:
734:
730:
727:
721:
720:
717:
711:
690:
685:
670:
664:
663:
661:
659:
655:
649:
647:Pauli matrices
643:
642:
640:
638:
631:
625:
624:
622:
617:
613:
610:
608:Matrix of ones
604:
603:
593:
572:
568:
566:
560:
559:
557:
552:
547:
543:
540:
534:
533:
526:
517: = (
512:
507:
505:
503:Hilbert matrix
499:
498:
491:
478:
473:
469:
462:
456:
455:
449:
447:
444:
438:
437:
431:
429:
422:
416:
415:
409:
407:
400:
394:
393:
390:
387:
384:
369:which is 1 if
356:
347:
341:
338:
318:
317:
303:
297:
294:
292:
289:
287:
284:
283:
280:
277:
275:
272:
270:
267:
266:
264:
259:
254:
251:
248:
244:
220:
217:
214:
199:
198:
187:
182:
176:
173:
171:
168:
166:
163:
161:
158:
157:
154:
151:
149:
146:
144:
141:
139:
136:
135:
132:
129:
127:
124:
122:
119:
117:
114:
113:
110:
107:
105:
102:
100:
97:
95:
92:
91:
89:
84:
79:
75:
13:
10:
9:
6:
4:
3:
2:
4553:
4542:
4539:
4537:
4534:
4533:
4531:
4521:
4515:
4511:
4507:
4503:
4502:
4498:
4484:
4480:
4474:
4471:
4460:
4456:
4449:
4447:
4443:
4439:
4433:
4430:
4424:
4419:
4413:
4408:
4404:
4401:
4400:
4396:
4391:
4387:
4383:
4380:
4377:
4373:
4369:
4366:
4363:
4359:
4358:Pseudoinverse
4356:
4354:
4351:
4348:
4344:
4341:
4338:
4334:
4330:
4327:
4324:
4321:
4320:
4316:
4311:
4310:Wilson matrix
4308:
4307:
4303:
4298:
4294:
4291:
4288:
4284:
4281:
4278:
4274:
4270:
4266:
4263:
4260:
4257:
4254:
4251:
4248:
4244:
4241:
4238:
4234:
4233:basis vectors
4230:
4226:
4222:
4219:
4216:
4212:
4209:
4206:
4202:
4198:
4195:
4192:
4188:
4184:
4180:
4177:
4174:
4170:
4167:
4164:
4160:
4157:
4154:
4150:
4147:
4144:
4140:
4136:
4132:
4129:
4126:
4122:
4118:
4115:
4114:
4110:
4105:
4102:
4099:
4095:
4088:
4084:
4081:
4078:
4074:
4071:
4068:
4065:
4062:
4058:
4054:
4051:
4048:
4045:
4042:
4038:
4037:Degree matrix
4035:
4032:
4028:
4024:
4021:
4019:are adjacent.
4018:
4014:
4010:
4003:
4000:
3999:
3998:
3996:
3992:
3984:
3979:
3976:
3974:
3970:
3969:probabilities
3966:
3963:
3960:
3956:
3952:
3949:
3946:
3942:
3938:
3934:
3931:
3928:
3925:
3922:
3919:
3916:
3913:
3910:
3906:
3902:
3899:
3896:
3892:
3889:
3886:
3882:
3878:
3874:
3871:
3868:
3864:
3860:
3856:
3853:
3850:
3847:
3844:
3840:
3837:
3836:
3835:
3833:
3829:
3821:
3814:
3799:
3794:
3790:
3786:
3783:
3778:
3775:
3767:
3764:
3759:
3755:
3748:
3745:
3737:
3735:
3732:
3731:
3728:
3726:
3722:
3718:
3716:
3713:
3712:
3709:
3707:
3703:
3701:
3698:
3697:
3693:
3689:
3687:
3683:
3681:
3678:
3677:
3674:
3671:
3668:
3666:
3663:
3662:
3659:
3657:
3653:
3651:
3648:
3647:
3644:
3641:
3638:
3634:
3632:
3629:
3628:
3625:
3623:
3619:
3617:
3614:
3613:
3610:
3607:
3605:
3602:
3601:
3598:
3595:
3591:
3587:
3583:
3581:
3580:Payoff matrix
3578:
3577:
3574:
3570:
3566:
3564:
3562:
3561:Moment matrix
3559:
3558:
3555:
3553:
3549:
3547:
3544:
3543:
3540:
3537:
3533:
3529:
3527:
3524:
3523:
3520:
3518:
3514:
3510:
3508:
3505:
3504:
3501:
3499:
3495:
3491:
3489:
3486:
3485:
3482:
3480:
3476:
3472:
3471:Coding theory
3468:
3466:
3463:
3462:
3459:
3457:
3453:
3451:
3448:
3447:
3444:
3440:
3438:
3434:
3430:
3428:
3425:
3424:
3420:
3417:
3415:
3411:
3409:
3406:
3405:
3402:
3400:
3399:Coxeter group
3396:
3392:
3390:
3387:
3386:
3383:
3381:
3377:
3375:
3372:
3371:
3368:
3364:
3361:
3358:
3354:
3350:
3348:
3345:
3344:
3341:
3339:
3335:
3331:
3329:
3328:Cartan matrix
3326:
3325:
3321:
3318:
3314:
3310:
3308:
3305:
3304:
3301:
3297:
3294:
3290:
3286:
3284:
3283:Bézout matrix
3281:
3280:
3276:
3272:
3269:
3267:
3264:
3263:
3260:
3256:
3252:
3250:
3246:
3243:
3241:
3238:
3237:
3233:
3230:
3227:
3226:
3220:
3213:
3209:
3206:
3204:
3201:
3200:
3196:
3192:
3190:
3188:
3185:
3184:
3181:
3178:
3176:
3173:
3172:
3169:
3166:
3164:
3161:
3160:
3157:
3154:
3152:
3149:
3148:
3144:
3140:
3136:
3133:
3129:
3127:
3124:
3123:
3120:
3117:
3116:Jordan blocks
3113:
3109:
3105:
3103:
3100:
3099:
3096:
3093:
3089:
3085:
3083:
3080:
3079:
3075:
3071:
3068:
3064:
3062:
3059:
3058:
3054:
3051:
3048:
3047:
3041:
3035:
3032:
3028:
3024:
3016:
3014:
3011:
3010:
3007:
3004:
3000:
2997:
2993:
2989:
2987:
2984:
2983:
2980:
2977:
2973:
2969:
2965:
2963:
2960:
2959:
2955:
2950:
2946:
2941:
2938:
2936:
2933:
2932:
2928:
2925:
2921:
2919:
2916:
2915:
2912:
2909:
2907:
2904:
2903:
2899:
2895:
2892:
2888:
2885:
2881:
2877:
2873:
2869:
2867:
2864:
2863:
2860:
2857:
2853:
2851:
2848:
2847:
2843:
2839:
2836:
2832:
2828:
2824:
2822:
2819:
2818:
2814:
2810:
2808:
2805:
2801:
2797:
2793:
2791:
2790:Normal matrix
2788:
2787:
2783:
2779:
2776:
2772:
2768:
2766:
2763:
2762:
2759:
2756:
2752:
2748:
2744:
2740:
2737:
2733:
2731:
2728:
2727:
2721:
2717:
2714:
2711:
2707:
2703:
2701:
2698:
2697:
2693:
2689:
2686:
2682:
2678:
2674:
2670:
2666:
2664:
2661:
2660:
2656:
2650:
2647:
2643:
2639:
2635:
2633:
2628:
2625:
2624:
2621:
2619:
2616:
2612:
2608:
2604:
2601:
2598:
2597:
2593:
2590:
2585:
2582:
2579:
2574:
2570:
2566:
2563:Two matrices
2562:
2560:
2557:
2556:
2552:
2548:
2543:
2539:
2537:
2533:
2530:
2529:
2525:
2522:
2519:
2518:
2515:
2513:
2509:
2505:
2501:
2497:
2493:
2489:
2485:
2481:
2477:
2473:
2469:
2465:
2461:
2457:
2453:
2434:
2429:
2426:
2423:
2419:
2413:
2410:
2407:
2403:
2397:
2392:
2389:
2386:
2382:
2378:
2373:
2370:
2367:
2359:
2349:
2348:
2347:
2345:
2341:
2337:
2333:
2329:
2325:
2321:
2317:
2313:
2309:
2301:
2294:
2292:
2289:
2288:
2285:
2282:
2280:
2277:
2276:
2273:
2270:
2266:
2262:
2258:
2256:
2253:
2252:
2249:
2245:
2243:X–Y–Z matrix
2242:
2241:
2238:
2235:
2233:
2230:
2229:
2226:
2223:
2221:
2218:
2217:
2214:
2211:
2207:
2205:
2202:
2201:
2198:
2195:
2193:
2190:
2189:
2186:
2182:
2178:
2174:
2169:
2165:
2161:
2157:
2153:
2149:
2145:
2143:
2140:
2139:
2135:
2132:
2130:
2129:Sparse matrix
2127:
2126:
2123:
2120:
2118:
2115:
2114:
2111:
2108:
2104:
2100:
2096:
2094:
2091:
2090:
2087:
2084:
2080:
2076:
2072:
2070:
2067:
2066:
2063:
2060:
2058:
2055:
2054:
2051:
2048:
2046:
2043:
2042:
2039:
2036:
2034:
2031:
2030:
2027:
2025:
2021:
2019:
2018:Random matrix
2016:
2015:
2012:
2009:
2005:
2003:
2000:
1999:
1996:
1993:
1991:
1988:
1987:
1984:
1981:
1977:
1975:
1972:
1971:
1968:
1963:
1959:
1955:
1951:
1947:
1944: =
1942:
1938:
1934:
1932:
1929:
1928:
1925:
1922:
1918:
1916:
1913:
1912:
1909:
1906:
1904:
1901:
1900:
1896:
1893:
1891:
1890:Parisi matrix
1888:
1887:
1883:
1879:
1876:
1874:
1871:
1870:
1866:
1863:
1859:
1855:
1851:
1847:
1843:
1839:
1836:
1835:
1831:
1828:
1824:
1820:
1816:
1812:
1808:
1804:
1801:
1800:
1797:
1794:
1792:
1789:
1788:
1785:
1782:
1778:
1774:
1770:
1768:
1765:
1764:
1760:
1756:
1753:
1751:
1748:
1747:
1744:
1741:
1739:
1736:
1735:
1732:
1729:
1727:
1726:Markov matrix
1724:
1723:
1719:
1715:
1711:
1707:
1706:binary matrix
1703:
1699:
1696:
1694:
1691:
1690:
1687:
1684:
1682:
1679:
1678:
1675:
1672:
1670:
1669:Hollow matrix
1667:
1666:
1663:
1660:
1658:
1655:
1654:
1651:
1648:
1644:
1640:
1636:
1634:
1631:
1630:
1626:
1623:
1621:
1620:Hankel matrix
1618:
1617:
1614:
1611:
1609:
1606:
1605:
1602:
1599:
1597:
1594:
1593:
1590:
1575:
1572:
1567:
1563:
1559:
1554:
1550:
1542:entry, where
1529:
1526:
1501:
1497:
1493:
1488:
1484:
1457:
1434:
1431:
1428:
1420:
1418:
1415:
1414:
1411:
1408:
1406:
1403:
1402:
1399:
1396:
1394:
1391:
1390:
1387:
1384:
1382:
1379:
1378:
1375:
1372:
1370:
1367:
1366:
1363:
1360:
1359:main diagonal
1356:
1354:
1351:
1350:
1347:
1325:
1322:
1318:
1307:
1304:
1301:
1297:
1293:
1283:
1280:
1276:
1262:
1260:
1257:
1256:
1253:
1251:
1235:
1232:
1227:
1223:
1219:
1213:
1207:
1199:
1195:
1193:
1190:
1189:
1186:
1183:
1181:
1178:
1177:
1174:
1171:
1169:
1166:
1165:
1162:
1159:
1157:
1154:
1153:
1150:
1147:
1145:
1142:
1141:
1138:
1133:
1129:
1125:
1121:
1117:
1114: =
1112:
1108:
1104:
1102:
1099:
1098:
1095:
1092:
1085:
1078:
1071:
1064:
1062:
1061:Cauchy matrix
1059:
1058:
1055:
1052:
1048:
1046:
1043:
1042:
1039:
1036:
1034:
1031:
1030:
1027:
1024:
1022:
1019:
1018:
1015:
1012:
1008:
1006:
1003:
1002:
999:
996:
994:
991:
990:
986:
982:
978:
975:
973:
972:Binary matrix
970:
969:
965:
962:
960:
957:
956:
953:
950:
946:
944:
941:
940:
937:
934:
932:
929:
928:
924:
920:
918:
916:
913:
912:
908:
904:
902:
900:
897:
896:
893:
890:
888:
885:
884:
881:
878:
876:
873:
872:
869:
866:
864:
861:
860:
856:
852:
851:binary matrix
848:
845:
843:
840:
839:
835:
832:
829:
828:
825:
822:
818:
814:
810:
806:
805:main diagonal
802:
794:
788:
785:
779:
776:
774:
771:
770:
766:
763:
759:
754:
746:
742:
737:
731:
728:
726:
723:
722:
718:
714:
710:
706:
702:
698:
693:
689:
686:
683:
679:
675:
671:
669:
666:
665:
662:
660:
654:
650:
648:
645:
644:
641:
639:
636:
632:
630:
629:Pascal matrix
627:
626:
623:
620:
614:
611:
609:
606:
605:
601:
598:
594:
591:
587:
583:
579:
575:
569:
567:
565:
564:Lehmer matrix
562:
561:
558:
555:
550:
544:
541:
539:
536:
535:
531:
530:Hankel matrix
527:
524:
521: +
520:
515:
511:
508:
506:
504:
501:
500:
496:
492:
489:
485:
481:
476:
470:
467:
466:binary matrix
463:
461:
458:
457:
454:
453:vectorization
450:
448:
445:
443:
440:
439:
436:
435:Vectorization
432:
430:
427:
423:
421:
418:
417:
414:
413:Vectorization
410:
408:
405:
401:
399:
396:
395:
391:
388:
385:
382:
381:
378:
376:
372:
368:
364:
359:
354:
350:
339:
337:
335:
331:
327:
323:
301:
295:
290:
285:
278:
273:
268:
262:
257:
252:
249:
246:
242:
234:
233:
232:
218:
215:
212:
205:of dimension
204:
185:
180:
174:
169:
164:
159:
152:
147:
142:
137:
130:
125:
120:
115:
108:
103:
98:
93:
87:
82:
77:
73:
65:
64:
63:
61:
57:
53:
49:
45:
41:
37:
33:
29:
20:
16:
4509:
4486:. Retrieved
4482:
4473:
4462:. Retrieved
4458:
4436:Hogben
4432:
4389:
4385:
4371:
4223:— a type of
4139:non-negative
4127:weak decays.
4124:
4104:Tutte matrix
4097:
4090:
4016:
4012:
4005:
3988:
3973:Markov chain
3955:non-negative
3944:
3940:
3936:
3908:
3904:
3894:
3884:
3876:
3858:
3825:
3650:Shear matrix
3635:A matrix in
3584:A matrix in
3193:Synonym for
3111:
3088:eigenvectors
3030:
3026:
3022:
3021:, such that
2975:
2971:
2948:
2944:
2890:
2886:
2883:
2834:
2830:
2806:
2803:
2799:
2781:
2774:
2770:
2754:
2749:denotes the
2746:
2742:
2738:
2735:
2709:
2705:
2684:
2680:
2676:
2672:
2645:
2641:
2637:
2617:
2614:
2610:
2588:
2583:
2580:
2577:
2572:
2568:
2564:
2546:
2541:
2511:
2507:
2503:
2499:
2495:
2491:
2487:
2483:
2482:) such that
2479:
2475:
2474:is a matrix
2471:
2463:
2459:
2451:
2449:
2343:
2339:
2335:
2331:
2327:
2323:
2319:
2315:
2311:
2305:
2279:Walsh matrix
2268:
2264:
2260:
2210:determinants
2180:
2176:
2172:
2167:
2163:
2159:
2155:
2151:
2106:
2102:
2082:
2078:
1961:
1957:
1953:
1949:
1945:
1940:
1936:
1882:block matrix
1881:
1880:Synonym for
1861:
1857:
1853:
1849:
1826:
1822:
1818:
1814:
1780:
1776:
1772:
1767:Moore matrix
1758:
1757:Synonym for
1713:
1709:
1705:
1702:(0,1)-matrix
1701:
1700:Synonym for
1646:
1642:
1249:
1197:
1131:
1127:
1123:
1119:
1115:
1110:
1106:
1087:
1080:
1073:
1066:
1021:Block matrix
1011:block matrix
984:
981:(0,1)-matrix
980:
979:Synonym for
948:
922:
921:Synonym for
906:
905:Synonym for
854:
850:
849:Synonym for
842:(0,1)-matrix
820:
816:
812:
800:
798:
780:
761:
757:
749:
744:
740:
732:
725:Shift matrix
712:
708:
704:
700:
696:
691:
687:
652:
615:
589:
585:
581:
577:
570:
553:
545:
522:
518:
513:
509:
487:
483:
479:
471:
377:and 0 else.
374:
370:
366:
362:
357:
345:
343:
319:
200:
55:
43:
25:
15:
4043:in a graph.
4015:and vertex
3881:covariances
3865:of several
3843:probability
3686:polynomials
3637:knot theory
3604:Pick matrix
3586:game theory
3479:linear code
3395:involutions
3289:determinant
3259:determinant
3074:eigenvalues
3067:zero matrix
3052:Explanation
2856:orthonormal
2523:Explanation
2506:inverse of
2456:commutative
2033:Sign matrix
2008:quaternions
1980:polynomials
1921:permutation
943:Band matrix
833:Explanation
773:Zero matrix
386:Explanation
322:eigenvalues
203:zero matrix
40:engineering
32:mathematics
4530:Categories
4499:References
4488:2020-09-07
4464:2020-09-07
4279:sequences.
4273:amino acid
4227:, used in
3921:Hat matrix
3828:statistics
3569:statistics
3536:hyperplane
3532:reflection
3231:Definition
3139:eigenbasis
3137:It has an
2999:relaxation
2992:unimodular
2675:such that
2575:such that
2510:, denoted
1417:GCD matrix
672:Encodes a
404:linear map
4382:Wronskian
4297:chemistry
4141:and with
4135:Hermitian
3776:−
3749:−
3590:economics
3441:See also
3363:Transpose
3353:cofactors
3298:See also
3293:resultant
3245:Transpose
3234:Comments
2827:transpose
2815:applies.
2600:EP matrix
2383:∑
2346:given by
2148:transpose
2099:transpose
1856:) or ker(
1821:) or ker(
1811:transpose
1573:∈
1432:×
1305:≠
1298:∑
695:are 1 if
334:chemistry
250:×
216:×
170:⋯
153:⋮
148:⋱
143:⋮
138:⋮
126:⋯
104:⋯
62:given by
4541:Matrices
4508:(2006),
4397:See also
4388:is the (
4293:Z-matrix
4243:S matrix
4057:vertices
3845:of each.
3622:rotation
3567:Used in
3212:M-matrix
3163:M-matrix
2947:−
2872:isometry
2858:vectors.
2291:Z-matrix
1718:relation
809:diagonal
699:divides
597:positive
584:) ÷ max(
201:and the
30:used in
28:matrices
4333:vectors
4239:system.
4237:quantum
4189:of the
3692:coprime
3365:of the
3336:, or a
3291:is the
3247:of the
3132:similar
2878:of its
2874:on the
2669:inverse
2468:inverse
2342:matrix
2334:is the
2330:matrix
2318:matrix
1519:as its
1447:matrix
1079:) for (
330:physics
326:product
56:entries
54:called
52:numbers
36:science
4516:
4193:SU(3).
4041:vertex
3433:points
3414:points
3357:minors
3315:of an
3055:Notes
3001:of an
2880:kernel
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2745:where
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2322:and a
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576:= min(
392:Notes
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