1075:
1111:
733:
127:
947:
166:
1038:
1152:
957:
723:
72:
whose eigenvalues have positive real parts. As it is a Z-matrix, its off-diagonal entries are less than or equal to zero.
1176:
135:
112:
758:
305:
522:
159:
597:
753:
275:
1145:
857:
728:
642:
962:
852:
560:
240:
39:
29:
997:
926:
808:
668:
265:
152:
867:
450:
255:
69:
1181:
813:
550:
400:
395:
230:
205:
200:
1138:
1118:
1007:
365:
195:
175:
21:
1126:
8:
1028:
1002:
580:
385:
375:
1079:
1033:
1023:
977:
972:
901:
837:
703:
440:
435:
370:
360:
225:
104:
58:
1171:
1090:
1074:
877:
872:
862:
842:
803:
798:
627:
622:
607:
602:
593:
588:
535:
430:
380:
325:
295:
290:
270:
260:
220:
131:
108:
1085:
1053:
982:
921:
916:
896:
832:
738:
708:
693:
673:
612:
540:
530:
501:
420:
415:
390:
320:
300:
210:
190:
36:
678:
783:
718:
698:
683:
663:
647:
545:
476:
466:
425:
310:
280:
1122:
1043:
987:
967:
952:
911:
788:
748:
713:
637:
576:
555:
496:
486:
471:
405:
350:
340:
335:
245:
86:
81:
61:
matrix, though the converse of this statement is not true in general for
1165:
1048:
906:
847:
778:
768:
763:
688:
617:
491:
481:
410:
330:
315:
250:
931:
888:
793:
506:
445:
355:
235:
46:
33:
773:
743:
511:
345:
215:
43:
17:
68:
From the above definition, a
Stieltjes matrix is a symmetric invertible
824:
285:
1058:
632:
992:
50:
144:
1110:
57:
Stieltjes matrix is invertible to a nonsingular symmetric
1163:
49:entries. A Stieltjes matrix is necessarily an
121:
98:
1146:
160:
124:Iterative Methods for Solving Linear Systems
1153:
1139:
734:Fundamental (linear differential equation)
167:
153:
101:Iterative Solution of Large Linear Systems
1039:Matrix representation of conic sections
1164:
148:
1105:
13:
174:
14:
1193:
1109:
1073:
941:Used in science and engineering
184:Explicitly constrained entries
1:
958:Fundamental (computer vision)
92:
1125:. You can help Knowledge by
7:
724:Duplication and elimination
523:eigenvalues or eigenvectors
75:
10:
1198:
1104:
657:With specific applications
286:Discrete Fourier Transform
1067:
1016:
948:Cabibbo–Kobayashi–Maskawa
940:
886:
822:
656:
575:Satisfying conditions on
574:
520:
459:
183:
1177:Numerical linear algebra
40:positive definite matrix
30:Thomas Joannes Stieltjes
306:Generalized permutation
122:Anne Greenbaum (1987).
99:David M. Young (2003).
1080:Mathematics portal
1117:This article about
1029:Linear independence
276:Diagonally dominant
65: > 2.
1034:Matrix exponential
1024:Jordan normal form
858:Fisher information
729:Euclidean distance
643:Totally unimodular
105:Dover Publications
1134:
1133:
1099:
1098:
1091:Category:Matrices
963:Fuzzy associative
853:Doubly stochastic
561:Positive-definite
241:Block tridiagonal
1189:
1155:
1148:
1141:
1113:
1106:
1086:List of matrices
1078:
1077:
1054:Row echelon form
998:State transition
927:Seidel adjacency
809:Totally positive
669:Alternating sign
266:Complex Hadamard
169:
162:
155:
146:
145:
141:
118:
26:Stieltjes matrix
1197:
1196:
1192:
1191:
1190:
1188:
1187:
1186:
1162:
1161:
1160:
1159:
1102:
1100:
1095:
1072:
1063:
1012:
936:
882:
818:
652:
570:
516:
455:
256:Centrosymmetric
179:
173:
138:
130:. p. 162.
115:
95:
78:
20:, particularly
12:
11:
5:
1195:
1185:
1184:
1179:
1174:
1158:
1157:
1150:
1143:
1135:
1132:
1131:
1114:
1097:
1096:
1094:
1093:
1088:
1083:
1068:
1065:
1064:
1062:
1061:
1056:
1051:
1046:
1044:Perfect matrix
1041:
1036:
1031:
1026:
1020:
1018:
1014:
1013:
1011:
1010:
1005:
1000:
995:
990:
985:
980:
975:
970:
965:
960:
955:
950:
944:
942:
938:
937:
935:
934:
929:
924:
919:
914:
909:
904:
899:
893:
891:
884:
883:
881:
880:
875:
870:
865:
860:
855:
850:
845:
840:
835:
829:
827:
820:
819:
817:
816:
814:Transformation
811:
806:
801:
796:
791:
786:
781:
776:
771:
766:
761:
756:
751:
746:
741:
736:
731:
726:
721:
716:
711:
706:
701:
696:
691:
686:
681:
676:
671:
666:
660:
658:
654:
653:
651:
650:
645:
640:
635:
630:
625:
620:
615:
610:
605:
600:
591:
585:
583:
572:
571:
569:
568:
563:
558:
553:
551:Diagonalizable
548:
543:
538:
533:
527:
525:
521:Conditions on
518:
517:
515:
514:
509:
504:
499:
494:
489:
484:
479:
474:
469:
463:
461:
457:
456:
454:
453:
448:
443:
438:
433:
428:
423:
418:
413:
408:
403:
401:Skew-symmetric
398:
396:Skew-Hermitian
393:
388:
383:
378:
373:
368:
363:
358:
353:
348:
343:
338:
333:
328:
323:
318:
313:
308:
303:
298:
293:
288:
283:
278:
273:
268:
263:
258:
253:
248:
243:
238:
233:
231:Block-diagonal
228:
223:
218:
213:
208:
206:Anti-symmetric
203:
201:Anti-Hermitian
198:
193:
187:
185:
181:
180:
172:
171:
164:
157:
149:
143:
142:
136:
119:
113:
107:. p. 42.
94:
91:
90:
89:
87:Metzler matrix
84:
82:Hurwitz matrix
77:
74:
28:, named after
9:
6:
4:
3:
2:
1194:
1183:
1180:
1178:
1175:
1173:
1170:
1169:
1167:
1156:
1151:
1149:
1144:
1142:
1137:
1136:
1130:
1128:
1124:
1120:
1115:
1112:
1108:
1107:
1103:
1092:
1089:
1087:
1084:
1082:
1081:
1076:
1070:
1069:
1066:
1060:
1057:
1055:
1052:
1050:
1049:Pseudoinverse
1047:
1045:
1042:
1040:
1037:
1035:
1032:
1030:
1027:
1025:
1022:
1021:
1019:
1017:Related terms
1015:
1009:
1008:Z (chemistry)
1006:
1004:
1001:
999:
996:
994:
991:
989:
986:
984:
981:
979:
976:
974:
971:
969:
966:
964:
961:
959:
956:
954:
951:
949:
946:
945:
943:
939:
933:
930:
928:
925:
923:
920:
918:
915:
913:
910:
908:
905:
903:
900:
898:
895:
894:
892:
890:
885:
879:
876:
874:
871:
869:
866:
864:
861:
859:
856:
854:
851:
849:
846:
844:
841:
839:
836:
834:
831:
830:
828:
826:
821:
815:
812:
810:
807:
805:
802:
800:
797:
795:
792:
790:
787:
785:
782:
780:
777:
775:
772:
770:
767:
765:
762:
760:
757:
755:
752:
750:
747:
745:
742:
740:
737:
735:
732:
730:
727:
725:
722:
720:
717:
715:
712:
710:
707:
705:
702:
700:
697:
695:
692:
690:
687:
685:
682:
680:
677:
675:
672:
670:
667:
665:
662:
661:
659:
655:
649:
646:
644:
641:
639:
636:
634:
631:
629:
626:
624:
621:
619:
616:
614:
611:
609:
606:
604:
601:
599:
595:
592:
590:
587:
586:
584:
582:
578:
573:
567:
564:
562:
559:
557:
554:
552:
549:
547:
544:
542:
539:
537:
534:
532:
529:
528:
526:
524:
519:
513:
510:
508:
505:
503:
500:
498:
495:
493:
490:
488:
485:
483:
480:
478:
475:
473:
470:
468:
465:
464:
462:
458:
452:
449:
447:
444:
442:
439:
437:
434:
432:
429:
427:
424:
422:
419:
417:
414:
412:
409:
407:
404:
402:
399:
397:
394:
392:
389:
387:
384:
382:
379:
377:
374:
372:
369:
367:
366:Pentadiagonal
364:
362:
359:
357:
354:
352:
349:
347:
344:
342:
339:
337:
334:
332:
329:
327:
324:
322:
319:
317:
314:
312:
309:
307:
304:
302:
299:
297:
294:
292:
289:
287:
284:
282:
279:
277:
274:
272:
269:
267:
264:
262:
259:
257:
254:
252:
249:
247:
244:
242:
239:
237:
234:
232:
229:
227:
224:
222:
219:
217:
214:
212:
209:
207:
204:
202:
199:
197:
196:Anti-diagonal
194:
192:
189:
188:
186:
182:
177:
170:
165:
163:
158:
156:
151:
150:
147:
139:
137:0-89871-396-X
133:
129:
125:
120:
116:
114:0-486-42548-7
110:
106:
102:
97:
96:
88:
85:
83:
80:
79:
73:
71:
66:
64:
60:
56:
52:
48:
45:
41:
38:
35:
31:
27:
23:
22:matrix theory
19:
1182:Matrix stubs
1127:expanding it
1116:
1101:
1071:
1003:Substitution
889:graph theory
565:
386:Quaternionic
376:Persymmetric
123:
100:
67:
62:
54:
47:off-diagonal
25:
15:
978:Hamiltonian
902:Biadjacency
838:Correlation
754:Householder
704:Commutation
441:Vandermonde
436:Tridiagonal
371:Permutation
361:Nonnegative
346:Matrix unit
226:Bisymmetric
59:nonnegative
44:nonpositive
18:mathematics
1166:Categories
878:Transition
873:Stochastic
843:Covariance
825:statistics
804:Symplectic
799:Similarity
628:Unimodular
623:Orthogonal
608:Involutory
603:Invertible
598:Projection
594:Idempotent
536:Convergent
431:Triangular
381:Polynomial
326:Hessenberg
296:Equivalent
291:Elementary
271:Copositive
261:Conference
221:Bidiagonal
93:References
1059:Wronskian
983:Irregular
973:Gell-Mann
922:Laplacian
917:Incidence
897:Adjacency
868:Precision
833:Centering
739:Generator
709:Confusion
694:Circulant
674:Augmented
633:Unipotent
613:Nilpotent
589:Congruent
566:Stieltjes
541:Defective
531:Companion
502:Redheffer
421:Symmetric
416:Sylvester
391:Signature
321:Hermitian
301:Frobenius
211:Arrowhead
191:Alternant
53:. Every
37:symmetric
1172:Matrices
1119:matrices
887:Used in
823:Used in
784:Rotation
759:Jacobian
719:Distance
699:Cofactor
684:Carleman
664:Adjugate
648:Weighing
581:inverses
577:products
546:Definite
477:Identity
467:Exchange
460:Constant
426:Toeplitz
311:Hadamard
281:Diagonal
76:See also
70:Z-matrix
51:M-matrix
988:Overlap
953:Density
912:Edmonds
789:Seifert
749:Hessian
714:Coxeter
638:Unitary
556:Hurwitz
487:Of ones
472:Hilbert
406:Skyline
351:Metzler
341:Logical
336:Integer
246:Boolean
178:classes
32:, is a
907:Degree
848:Design
779:Random
769:Payoff
764:Moment
689:Cartan
679:BĂ©zout
618:Normal
492:Pascal
482:Lehmer
411:Sparse
331:Hollow
316:Hankel
251:Cauchy
176:Matrix
134:
111:
1121:is a
968:Gamma
932:Tutte
794:Shear
507:Shift
497:Pauli
446:Walsh
356:Moore
236:Block
42:with
1123:stub
774:Pick
744:Gram
512:Zero
216:Band
132:ISBN
128:SIAM
109:ISBN
34:real
24:, a
863:Hat
596:or
579:or
55:nĂ—n
16:In
1168::
126:.
103:.
1154:e
1147:t
1140:v
1129:.
993:S
451:Z
168:e
161:t
154:v
140:.
117:.
63:n
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