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Copositive matrix

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1096: 1132: 77: 754: 106: 968: 187: 1059: 1173: 978: 744: 150: 779: 326: 543: 180: 618: 774: 296: 1166: 878: 749: 663: 1197: 983: 873: 581: 261: 113: 1018: 947: 829: 689: 286: 173: 888: 471: 276: 1202: 834: 571: 421: 416: 251: 226: 221: 1095: 1159: 1139: 1028: 386: 216: 196: 27: 1049: 1023: 601: 406: 396: 120: 43: 1100: 1054: 1044: 998: 993: 922: 858: 724: 461: 456: 391: 381: 246: 159: 134: 1192: 1111: 898: 893: 883: 863: 824: 819: 648: 643: 628: 623: 614: 609: 556: 451: 401: 346: 316: 311: 281: 241: 146: 1143: 85: 1106: 1074: 1003: 942: 937: 917: 853: 759: 729: 714: 699: 694: 633: 586: 561: 551: 522: 441: 436: 411: 341: 321: 231: 211: 804: 739: 719: 704: 684: 668: 566: 497: 487: 446: 331: 301: 1064: 1008: 988: 973: 932: 809: 769: 734: 658: 597: 576: 517: 507: 492: 426: 371: 361: 356: 266: 139: 20: 1186: 1069: 927: 868: 799: 789: 784: 709: 638: 512: 502: 431: 351: 336: 271: 952: 909: 814: 527: 466: 376: 256: 794: 764: 532: 366: 236: 109: 24: 845: 306: 1079: 653: 1013: 1131: 165: 169: 1147: 88: 46: 119:
Copositive matrices find applications in economics,
1037: 961: 907: 843: 677: 595: 541: 480: 204: 138: 108:. The collection of all copositive matrices is a 100: 71: 141:Nonnegative Matrices in the Mathematical Sciences 112:; it includes as a subset the collection of real 1167: 181: 8: 1174: 1160: 755:Fundamental (linear differential equation) 188: 174: 166: 87: 51: 45: 1060:Matrix representation of conic sections 7: 1128: 1126: 1146:. You can help Knowledge (XXG) by 14: 1130: 1094: 962:Used in science and engineering 205:Explicitly constrained entries 1: 979:Fundamental (computer vision) 82:for every nonnegative vector 72:{\displaystyle x^{T}Ax\geq 0} 19:In mathematics, specifically 745:Duplication and elimination 544:eigenvalues or eigenvectors 1219: 1125: 678:With specific applications 307:Discrete Fourier Transform 114:positive-definite matrices 1088: 969:Cabibbo–Kobayashi–Maskawa 596:Satisfying conditions on 16:Matrix in linear algebra 327:Generalized permutation 101:{\displaystyle x\geq 0} 1101:Mathematics portal 102: 73: 103: 74: 86: 44: 1138:This article about 1050:Linear independence 297:Diagonally dominant 121:operations research 1055:Matrix exponential 1045:Jordan normal form 879:Fisher information 750:Euclidean distance 664:Totally unimodular 145:. Academic Press. 135:Robert J. Plemmons 123:, and statistics. 98: 69: 1155: 1154: 1120: 1119: 1112:Category:Matrices 984:Fuzzy associative 874:Doubly stochastic 582:Positive-definite 262:Block tridiagonal 160:Copositive matrix 133:Berman, Abraham; 1210: 1176: 1169: 1162: 1134: 1127: 1107:List of matrices 1099: 1098: 1075:Row echelon form 1019:State transition 948:Seidel adjacency 830:Totally positive 690:Alternating sign 287:Complex Hadamard 190: 183: 176: 167: 156: 144: 107: 105: 104: 99: 78: 76: 75: 70: 56: 55: 1218: 1217: 1213: 1212: 1211: 1209: 1208: 1207: 1198:Convex analysis 1183: 1182: 1181: 1180: 1123: 1121: 1116: 1093: 1084: 1033: 957: 903: 839: 673: 591: 537: 476: 277:Centrosymmetric 200: 194: 153: 132: 129: 84: 83: 47: 42: 41: 17: 12: 11: 5: 1216: 1214: 1206: 1205: 1200: 1195: 1185: 1184: 1179: 1178: 1171: 1164: 1156: 1153: 1152: 1135: 1118: 1117: 1115: 1114: 1109: 1104: 1089: 1086: 1085: 1083: 1082: 1077: 1072: 1067: 1065:Perfect matrix 1062: 1057: 1052: 1047: 1041: 1039: 1035: 1034: 1032: 1031: 1026: 1021: 1016: 1011: 1006: 1001: 996: 991: 986: 981: 976: 971: 965: 963: 959: 958: 956: 955: 950: 945: 940: 935: 930: 925: 920: 914: 912: 905: 904: 902: 901: 896: 891: 886: 881: 876: 871: 866: 861: 856: 850: 848: 841: 840: 838: 837: 835:Transformation 832: 827: 822: 817: 812: 807: 802: 797: 792: 787: 782: 777: 772: 767: 762: 757: 752: 747: 742: 737: 732: 727: 722: 717: 712: 707: 702: 697: 692: 687: 681: 679: 675: 674: 672: 671: 666: 661: 656: 651: 646: 641: 636: 631: 626: 621: 612: 606: 604: 593: 592: 590: 589: 584: 579: 574: 572:Diagonalizable 569: 564: 559: 554: 548: 546: 542:Conditions on 539: 538: 536: 535: 530: 525: 520: 515: 510: 505: 500: 495: 490: 484: 482: 478: 477: 475: 474: 469: 464: 459: 454: 449: 444: 439: 434: 429: 424: 422:Skew-symmetric 419: 417:Skew-Hermitian 414: 409: 404: 399: 394: 389: 384: 379: 374: 369: 364: 359: 354: 349: 344: 339: 334: 329: 324: 319: 314: 309: 304: 299: 294: 289: 284: 279: 274: 269: 264: 259: 254: 252:Block-diagonal 249: 244: 239: 234: 229: 227:Anti-symmetric 224: 222:Anti-Hermitian 219: 214: 208: 206: 202: 201: 195: 193: 192: 185: 178: 170: 164: 163: 157: 151: 128: 125: 97: 94: 91: 80: 79: 68: 65: 62: 59: 54: 50: 21:linear algebra 15: 13: 10: 9: 6: 4: 3: 2: 1215: 1204: 1201: 1199: 1196: 1194: 1191: 1190: 1188: 1177: 1172: 1170: 1165: 1163: 1158: 1157: 1151: 1149: 1145: 1141: 1136: 1133: 1129: 1124: 1113: 1110: 1108: 1105: 1103: 1102: 1097: 1091: 1090: 1087: 1081: 1078: 1076: 1073: 1071: 1070:Pseudoinverse 1068: 1066: 1063: 1061: 1058: 1056: 1053: 1051: 1048: 1046: 1043: 1042: 1040: 1038:Related terms 1036: 1030: 1029:Z (chemistry) 1027: 1025: 1022: 1020: 1017: 1015: 1012: 1010: 1007: 1005: 1002: 1000: 997: 995: 992: 990: 987: 985: 982: 980: 977: 975: 972: 970: 967: 966: 964: 960: 954: 951: 949: 946: 944: 941: 939: 936: 934: 931: 929: 926: 924: 921: 919: 916: 915: 913: 911: 906: 900: 897: 895: 892: 890: 887: 885: 882: 880: 877: 875: 872: 870: 867: 865: 862: 860: 857: 855: 852: 851: 849: 847: 842: 836: 833: 831: 828: 826: 823: 821: 818: 816: 813: 811: 808: 806: 803: 801: 798: 796: 793: 791: 788: 786: 783: 781: 778: 776: 773: 771: 768: 766: 763: 761: 758: 756: 753: 751: 748: 746: 743: 741: 738: 736: 733: 731: 728: 726: 723: 721: 718: 716: 713: 711: 708: 706: 703: 701: 698: 696: 693: 691: 688: 686: 683: 682: 680: 676: 670: 667: 665: 662: 660: 657: 655: 652: 650: 647: 645: 642: 640: 637: 635: 632: 630: 627: 625: 622: 620: 616: 613: 611: 608: 607: 605: 603: 599: 594: 588: 585: 583: 580: 578: 575: 573: 570: 568: 565: 563: 560: 558: 555: 553: 550: 549: 547: 545: 540: 534: 531: 529: 526: 524: 521: 519: 516: 514: 511: 509: 506: 504: 501: 499: 496: 494: 491: 489: 486: 485: 483: 479: 473: 470: 468: 465: 463: 460: 458: 455: 453: 450: 448: 445: 443: 440: 438: 435: 433: 430: 428: 425: 423: 420: 418: 415: 413: 410: 408: 405: 403: 400: 398: 395: 393: 390: 388: 387:Pentadiagonal 385: 383: 380: 378: 375: 373: 370: 368: 365: 363: 360: 358: 355: 353: 350: 348: 345: 343: 340: 338: 335: 333: 330: 328: 325: 323: 320: 318: 315: 313: 310: 308: 305: 303: 300: 298: 295: 293: 290: 288: 285: 283: 280: 278: 275: 273: 270: 268: 265: 263: 260: 258: 255: 253: 250: 248: 245: 243: 240: 238: 235: 233: 230: 228: 225: 223: 220: 218: 217:Anti-diagonal 215: 213: 210: 209: 207: 203: 198: 191: 186: 184: 179: 177: 172: 171: 168: 162:at PlanetMath 161: 158: 154: 152:0-12-092250-9 148: 143: 142: 136: 131: 130: 126: 124: 122: 117: 115: 111: 95: 92: 89: 66: 63: 60: 57: 52: 48: 40: 39: 38: 36: 32: 29: 26: 22: 1203:Matrix stubs 1148:expanding it 1137: 1122: 1092: 1024:Substitution 910:graph theory 407:Quaternionic 397:Persymmetric 291: 140: 118: 81: 34: 30: 18: 999:Hamiltonian 923:Biadjacency 859:Correlation 775:Householder 725:Commutation 462:Vandermonde 457:Tridiagonal 392:Permutation 382:Nonnegative 367:Matrix unit 247:Bisymmetric 110:proper cone 1187:Categories 899:Transition 894:Stochastic 864:Covariance 846:statistics 825:Symplectic 820:Similarity 649:Unimodular 644:Orthogonal 629:Involutory 624:Invertible 619:Projection 615:Idempotent 557:Convergent 452:Triangular 402:Polynomial 347:Hessenberg 317:Equivalent 312:Elementary 292:Copositive 282:Conference 242:Bidiagonal 127:References 35:copositive 1080:Wronskian 1004:Irregular 994:Gell-Mann 943:Laplacian 938:Incidence 918:Adjacency 889:Precision 854:Centering 760:Generator 730:Confusion 715:Circulant 695:Augmented 654:Unipotent 634:Nilpotent 610:Congruent 587:Stieltjes 562:Defective 552:Companion 523:Redheffer 442:Symmetric 437:Sylvester 412:Signature 342:Hermitian 322:Frobenius 232:Arrowhead 212:Alternant 93:≥ 64:≥ 1193:Matrices 1140:matrices 908:Used in 844:Used in 805:Rotation 780:Jacobian 740:Distance 720:Cofactor 705:Carleman 685:Adjugate 669:Weighing 602:inverses 598:products 567:Definite 498:Identity 488:Exchange 481:Constant 447:Toeplitz 332:Hadamard 302:Diagonal 137:(1979). 1009:Overlap 974:Density 933:Edmonds 810:Seifert 770:Hessian 735:Coxeter 659:Unitary 577:Hurwitz 508:Of ones 493:Hilbert 427:Skyline 372:Metzler 362:Logical 357:Integer 267:Boolean 199:classes 928:Degree 869:Design 800:Random 790:Payoff 785:Moment 710:Cartan 700:BĂ©zout 639:Normal 513:Pascal 503:Lehmer 432:Sparse 352:Hollow 337:Hankel 272:Cauchy 197:Matrix 149:  28:matrix 1142:is a 989:Gamma 953:Tutte 815:Shear 528:Shift 518:Pauli 467:Walsh 377:Moore 257:Block 1144:stub 795:Pick 765:Gram 533:Zero 237:Band 147:ISBN 25:real 23:, a 884:Hat 617:or 600:or 37:if 33:is 1189:: 116:. 1175:e 1168:t 1161:v 1150:. 1014:S 472:Z 189:e 182:t 175:v 155:. 96:0 90:x 67:0 61:x 58:A 53:T 49:x 31:A

Index

linear algebra
real
matrix
proper cone
positive-definite matrices
operations research
Robert J. Plemmons
Nonnegative Matrices in the Mathematical Sciences
ISBN
0-12-092250-9
Copositive matrix
v
t
e
Matrix
Alternant
Anti-diagonal
Anti-Hermitian
Anti-symmetric
Arrowhead
Band
Bidiagonal
Bisymmetric
Block-diagonal
Block
Block tridiagonal
Boolean
Cauchy
Centrosymmetric
Conference

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