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Outline of linear algebra

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This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices.
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algebra 456:Householder transformation 42:System of linear equations 1321: 1059: 937: 895:Glossary of tensor theory 859:Projective transformation 636:Category of vector spaces 546:Examples of vector spaces 451:Elementary row operations 116:Characteristic polynomial 817:Affine coordinate system 648:Topological vector space 475:Woodbury matrix identity 251:Perron–Frobenius theorem 74:Gauss–Jordan elimination 869:Projective linear group 560:Galilean transformation 131:Cayley–Hamilton theorem 1028:Row and column vectors 707:Orientation (geometry) 690:Pseudo-Euclidean space 569:Lorentz transformation 353:Cholesky decomposition 1033:Row and column spaces 978:Scalar multiplication 802:Affine transformation 678:Orthogonal projection 673:Orthogonal complement 581:Row and column spaces 507:Scalar multiplication 342:Matrix decompositions 270:Diagonalizable matrix 199:Skew-symmetric matrix 106:Matrix multiplication 1168:Gram–Schmidt process 1120:Gaussian elimination 719:Symplectic structure 607:Rank–nullity theorem 470:Gram–Schmidt process 465:linear least squares 434:Matrix consimilarity 347:Matrix decomposition 218:Antihermitian matrix 69:Gaussian elimination 57:Cauchy–Binet formula 1298:Numerical stability 1178:Multilinear algebra 1153:Inner product space 1003:Linear independence 864:Projective geometry 730:Multilinear algebra 725:Multilinear algebra 658:Inner product space 653:Normed vector space 502:Linear independence 395:Schur decomposition 368:Polar decomposition 204:Conjugate transpose 146:Weyr canonical form 1008:Linear combination 492:Linear combination 419:Matrix equivalence 307:Vandermonde matrix 282:Tridiagonal matrix 141:Jordan normal form 136:Spread of a matrix 84:Strassen algorithm 1339: 1338: 1206:Geometric algebra 1163:Kronecker product 998:Linear projection 983:Vector projection 783:Geometric algebra 773:Symmetric algebra 712:Improper rotation 629:Linear functional 429:Matrix similarity 424:Matrix congruence 373:Reducing subspace 312:Stochastic matrix 297:Hessenberg matrix 277:Triangular matrix 227:Positive-definite 194:Orthogonal matrix 162:invertible matrix 16:(Redirected from 1369: 1329: 1328: 1211:Exterior algebra 1148:Hadamard product 1065: 1053:Linear equations 924: 917: 910: 901: 853:Projective space 848:Projective space 778:Clifford algebra 768:Exterior algebra 683:Orthogonal group 400:Schur complement 378:Spectral theorem 363:QR decomposition 358:LU decomposition 322:Circulant matrix 256:List of matrices 246:Spectral theorem 214:Hermitian matrix 189:Symmetric matrix 158:Matrix inversion 79:Overcompleteness 31:Linear equations 21: 1377: 1376: 1372: 1371: 1370: 1368: 1367: 1366: 1342: 1341: 1340: 1335: 1317: 1279: 1235: 1172: 1124: 1066: 1057: 1023:Change of basis 1013:Multilinear map 951: 933: 928: 886: 850: 832:Euclidean group 822:Flat (geometry) 812:Affine geometry 793: 751:Gamas's Theorem 727: 663:Euclidean space 644: 624:Linear function 612:Nullity theorem 596:Cyclic subspace 576:Linear subspace 565:Squeeze mapping 539:Hamel dimension 517:Change of basis 483: 447: 439:Row equivalence 415: 344: 317:Toeplitz matrix 261:Diagonal matrix 101:Matrix addition 92: 36:Linear equation 33: 23: 22: 15: 12: 11: 5: 1375: 1373: 1365: 1364: 1359: 1354: 1352:Linear algebra 1344: 1343: 1337: 1336: 1334: 1333: 1322: 1319: 1318: 1316: 1315: 1310: 1305: 1300: 1295: 1293:Floating-point 1289: 1287: 1281: 1280: 1278: 1277: 1275:Tensor product 1272: 1267: 1262: 1260:Function space 1257: 1252: 1246: 1244: 1237: 1236: 1234: 1233: 1228: 1223: 1218: 1213: 1208: 1203: 1198: 1196:Triple product 1193: 1188: 1182: 1180: 1174: 1173: 1171: 1170: 1165: 1160: 1155: 1150: 1145: 1140: 1134: 1132: 1126: 1125: 1123: 1122: 1117: 1112: 1110:Transformation 1107: 1102: 1100:Multiplication 1097: 1092: 1087: 1082: 1076: 1074: 1068: 1067: 1060: 1058: 1056: 1055: 1050: 1045: 1040: 1035: 1030: 1025: 1020: 1015: 1010: 1005: 1000: 995: 990: 985: 980: 975: 970: 965: 959: 957: 956:Basic concepts 953: 952: 950: 949: 944: 938: 935: 934: 931:Linear algebra 929: 927: 926: 919: 912: 904: 898: 897: 892: 885: 882: 881: 880: 871: 866: 861: 849: 846: 845: 844: 842:Galilean group 839: 837:Poincaré group 834: 829: 824: 819: 814: 809: 804: 792: 789: 788: 787: 786: 785: 780: 775: 770: 763:Tensor algebra 760: 755: 754: 753: 748: 743: 726: 723: 722: 721: 716: 715: 714: 704: 703: 702: 697: 687: 686: 685: 680: 675: 670: 665: 655: 650: 643: 640: 639: 638: 633: 632: 631: 626: 616: 615: 614: 609: 604: 598: 593: 588: 583: 573: 572: 571: 562: 548: 543: 542: 541: 531: 526: 525: 524: 519: 509: 504: 499: 494: 482: 479: 478: 477: 472: 467: 458: 453: 446: 443: 442: 441: 436: 431: 426: 421: 414: 411: 410: 409: 408: 407: 402: 392: 391: 390: 380: 375: 370: 365: 360: 355: 343: 340: 339: 338: 337: 336: 331: 326: 325: 324: 314: 309: 304: 302:Hessian matrix 299: 294: 289: 284: 279: 274: 273: 272: 253: 248: 243: 238: 233: 224: 223: 222: 221: 220: 211: 209:Unitary matrix 201: 196: 191: 186: 176: 171: 170: 169: 155: 150: 149: 148: 143: 138: 133: 123: 118: 113: 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1014: 1011: 1009: 1006: 1004: 1001: 999: 996: 994: 991: 989: 986: 984: 981: 979: 976: 974: 971: 969: 966: 964: 961: 960: 958: 954: 948: 945: 943: 940: 939: 936: 932: 925: 920: 918: 913: 911: 906: 905: 902: 896: 893: 891: 888: 887: 883: 879: 878:conic section 875: 872: 870: 867: 865: 862: 860: 857: 856: 855: 854: 847: 843: 840: 838: 835: 833: 830: 828: 825: 823: 820: 818: 815: 813: 810: 808: 805: 803: 800: 799: 798: 797: 790: 784: 781: 779: 776: 774: 771: 769: 766: 765: 764: 761: 759: 758:Outer product 756: 752: 749: 747: 744: 742: 739: 738: 737: 734: 733: 732: 731: 724: 720: 717: 713: 710: 709: 708: 705: 701: 698: 696: 693: 692: 691: 688: 684: 681: 679: 676: 674: 671: 669: 668:Orthogonality 666: 664: 661: 660: 659: 656: 654: 651: 649: 646: 645: 641: 637: 634: 630: 627: 625: 622: 621: 620: 617: 613: 610: 608: 605: 602: 599: 597: 594: 592: 589: 587: 584: 582: 579: 578: 577: 574: 570: 566: 563: 561: 557: 556:Shear mapping 554: 553: 552: 549: 547: 544: 540: 537: 536: 535: 532: 530: 527: 523: 520: 518: 515: 514: 513: 510: 508: 505: 503: 500: 498: 495: 493: 490: 489: 488: 487: 481:Vector spaces 480: 476: 473: 471: 468: 466: 462: 461:Least squares 459: 457: 454: 452: 449: 448: 444: 440: 437: 435: 432: 430: 427: 425: 422: 420: 417: 416: 412: 406: 403: 401: 398: 397: 396: 393: 389: 386: 385: 384: 381: 379: 376: 374: 371: 369: 366: 364: 361: 359: 356: 354: 351: 350: 349: 348: 341: 335: 332: 330: 329:Hankel matrix 327: 323: 320: 319: 318: 315: 313: 310: 308: 305: 303: 300: 298: 295: 293: 292:Sparse matrix 290: 288: 285: 283: 280: 278: 275: 271: 268: 267: 266: 265:main diagonal 262: 259: 258: 257: 254: 252: 249: 247: 244: 242: 239: 237: 234: 232: 228: 225: 219: 215: 212: 210: 207: 206: 205: 202: 200: 197: 195: 192: 190: 187: 185: 182: 181: 180: 177: 175: 172: 168: 167:Pseudoinverse 165: 164: 163: 159: 156: 154: 151: 147: 144: 142: 139: 137: 134: 132: 129: 128: 127: 124: 122: 119: 117: 114: 112: 109: 107: 104: 102: 99: 98: 97: 96: 89: 85: 82: 80: 77: 75: 72: 70: 67: 65: 64:Cramer's rule 62: 58: 55: 53: 50: 49: 48: 45: 43: 40: 39: 38: 37: 30: 28: 19: 1241:Vector space 973:Vector space 941: 851: 807:Affine group 796:Affine space 794: 728: 586:Column space 486:Vector space 484: 445:Computations 345: 334:(0,1)-matrix 287:Block matrix 93: 34: 26: 1221:Multivector 1186:Determinant 1143:Dot product 988:Linear span 695:Null vector 522:Hamel basis 497:Linear span 184:Dot product 47:Determinant 1346:Categories 1255:Direct sum 1090:Invertible 993:Linear map 642:Structures 619:Dual space 601:Null space 551:Linear map 241:Projection 1285:Numerical 1048:Transpose 603:, nullity 591:Row space 413:Relations 179:Transpose 1362:Outlines 1331:Category 1270:Subspace 1265:Quotient 1216:Bivector 1130:Bilinear 1072:Matrices 947:Glossary 884:See also 236:Pfaffian 174:Adjugate 90:Matrices 942:Outline 874:Quadric 1226:Tensor 1038:Kernel 968:Vector 963:Scalar 736:Tensor 95:Matrix 1095:Minor 1080:Block 1018:Basis 512:Basis 121:Trace 52:Minor 1250:Dual 1105:Rank 876:and 153:Rank 567:or 558:or 1348:: 463:, 263:, 229:, 216:, 160:, 923:e 916:t 909:v 20:)

Index

List of linear algebra topics
Linear equation
System of linear equations
Determinant
Minor
Cauchy–Binet formula
Cramer's rule
Gaussian elimination
Gauss–Jordan elimination
Overcompleteness
Strassen algorithm
Matrix
Matrix addition
Matrix multiplication
Basis transformation matrix
Characteristic polynomial
Trace
Eigenvalue, eigenvector and eigenspace
Cayley–Hamilton theorem
Spread of a matrix
Jordan normal form
Weyr canonical form
Rank
Matrix inversion
invertible matrix
Pseudoinverse
Adjugate
Transpose
Dot product
Symmetric matrix

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