1127:
1163:
42:
with a row and column for each vertex, having 0 on the diagonal, −1 for positions whose rows and columns correspond to adjacent vertices, and +1 for positions corresponding to non-adjacent vertices. It is also called the
90:
785:
999:
218:
1090:
175:(Proceedings, Rome, 1973), vol. I, pp. 481–511. Atti dei Convegni Lincei, No. 17. Accademia Nazionale dei Lincei, Rome.
1204:
1009:
775:
1223:
810:
357:
574:
211:
32:
1233:
649:
805:
327:
909:
780:
694:
1197:
1014:
904:
612:
292:
189:
Seidel, J. J. (1968), Strongly
Regular Graphs with (−1,1,0) Adjacency Matrix Having Eigenvalue 3.
1178:
1049:
860:
720:
317:
204:
919:
502:
307:
148:
865:
602:
452:
447:
282:
257:
252:
95:
1059:
417:
247:
227:
8:
1190:
1080:
1054:
632:
437:
427:
160:
van Lint, J. H., and Seidel, J. J. (1966), Equilateral point sets in elliptic geometry.
1131:
1085:
1075:
1029:
1024:
953:
889:
755:
492:
487:
422:
412:
277:
1228:
1142:
1126:
929:
924:
914:
894:
855:
850:
679:
674:
659:
654:
645:
640:
587:
482:
432:
377:
347:
342:
322:
312:
272:
1137:
1105:
1034:
973:
968:
948:
884:
790:
760:
745:
725:
664:
617:
592:
582:
553:
472:
467:
442:
372:
352:
262:
242:
60:
52:
39:
730:
835:
770:
750:
735:
715:
699:
597:
528:
518:
477:
362:
332:
1174:
1095:
1039:
1019:
1004:
963:
840:
800:
765:
689:
628:
607:
548:
538:
523:
457:
402:
392:
387:
297:
99:
86:
1217:
1100:
958:
899:
830:
820:
815:
740:
669:
543:
533:
462:
382:
367:
302:
179:
147:
The eigenvalue properties of the Seidel matrix are valuable in the study of
1170:
983:
940:
845:
558:
497:
407:
287:
186:. Boston: Academic Press. Many of the articles involve the Seidel matrix.
112:
24:
825:
795:
563:
397:
267:
20:
876:
337:
75:
1110:
684:
130:
1044:
71:
196:
104:
in 1966 and extensively exploited by Seidel and coauthors.
1162:
184:
51:. It can be interpreted as the result of subtracting the
129:
are positive. It is also the adjacency matrix of the
47:
or—its original name—the (−1,1,0)-
171:Seidel, J. J. (1976), A survey of two-graphs. In:
173:Colloquio Internazionale sulle Teorie Combinatorie
1215:
1198:
212:
1205:
1191:
786:Fundamental (linear differential equation)
219:
205:
1091:Matrix representation of conic sections
1216:
200:
1157:
85:The Seidel matrix was introduced by
16:Matrix in graph theory (mathematics)
191:Linear Algebra and its Applications
13:
226:
125:are negative and the edges not in
111:is also the adjacency matrix of a
14:
1245:
59:from the adjacency matrix of the
1161:
1125:
166:Proc. Kon. Ned. Aka. Wet. Ser. A
993:Used in science and engineering
236:Explicitly constrained entries
1:
1010:Fundamental (computer vision)
168:, vol. 69), pp. 335–348.
154:
78:of this matrix is called the
1177:. You can help Knowledge by
7:
776:Duplication and elimination
575:eigenvalues or eigenvectors
10:
1250:
1156:
709:With specific applications
338:Discrete Fourier Transform
178:Seidel, J. J. (1991), ed.
1119:
1068:
1000:Cabibbo–Kobayashi–Maskawa
992:
938:
874:
708:
627:Satisfying conditions on
626:
572:
511:
235:
162:Indagationes Mathematicae
358:Generalized permutation
149:strongly regular graphs
33:simple undirected graph
29:Seidel adjacency matrix
1224:Algebraic graph theory
1173:-related article is a
1132:Mathematics portal
121:in which the edges of
113:signed complete graph
107:The Seidel matrix of
1081:Linear independence
328:Diagonally dominant
1234:Graph theory stubs
1086:Matrix exponential
1076:Jordan normal form
910:Fisher information
781:Euclidean distance
695:Totally unimodular
91:Johan Jacob Seidel
1186:
1185:
1151:
1150:
1143:Category:Matrices
1015:Fuzzy associative
905:Doubly stochastic
613:Positive-definite
293:Block tridiagonal
1241:
1207:
1200:
1193:
1165:
1158:
1138:List of matrices
1130:
1129:
1106:Row echelon form
1050:State transition
979:Seidel adjacency
861:Totally positive
721:Alternating sign
318:Complex Hadamard
221:
214:
207:
198:
197:
185:
174:
133:associated with
103:
53:adjacency matrix
49:adjacency matrix
40:symmetric matrix
1249:
1248:
1244:
1243:
1242:
1240:
1239:
1238:
1214:
1213:
1212:
1211:
1154:
1152:
1147:
1124:
1115:
1064:
988:
934:
870:
704:
622:
568:
507:
308:Centrosymmetric
231:
225:
183:
182:and R. Mathon,
172:
157:
142:
119:
93:
80:Seidel spectrum
17:
12:
11:
5:
1247:
1237:
1236:
1231:
1226:
1210:
1209:
1202:
1195:
1187:
1184:
1183:
1166:
1149:
1148:
1146:
1145:
1140:
1135:
1120:
1117:
1116:
1114:
1113:
1108:
1103:
1098:
1096:Perfect matrix
1093:
1088:
1083:
1078:
1072:
1070:
1066:
1065:
1063:
1062:
1057:
1052:
1047:
1042:
1037:
1032:
1027:
1022:
1017:
1012:
1007:
1002:
996:
994:
990:
989:
987:
986:
981:
976:
971:
966:
961:
956:
951:
945:
943:
936:
935:
933:
932:
927:
922:
917:
912:
907:
902:
897:
892:
887:
881:
879:
872:
871:
869:
868:
866:Transformation
863:
858:
853:
848:
843:
838:
833:
828:
823:
818:
813:
808:
803:
798:
793:
788:
783:
778:
773:
768:
763:
758:
753:
748:
743:
738:
733:
728:
723:
718:
712:
710:
706:
705:
703:
702:
697:
692:
687:
682:
677:
672:
667:
662:
657:
652:
643:
637:
635:
624:
623:
621:
620:
615:
610:
605:
603:Diagonalizable
600:
595:
590:
585:
579:
577:
573:Conditions on
570:
569:
567:
566:
561:
556:
551:
546:
541:
536:
531:
526:
521:
515:
513:
509:
508:
506:
505:
500:
495:
490:
485:
480:
475:
470:
465:
460:
455:
453:Skew-symmetric
450:
448:Skew-Hermitian
445:
440:
435:
430:
425:
420:
415:
410:
405:
400:
395:
390:
385:
380:
375:
370:
365:
360:
355:
350:
345:
340:
335:
330:
325:
320:
315:
310:
305:
300:
295:
290:
285:
283:Block-diagonal
280:
275:
270:
265:
260:
258:Anti-symmetric
255:
253:Anti-Hermitian
250:
245:
239:
237:
233:
232:
224:
223:
216:
209:
201:
195:
194:
187:
176:
169:
156:
153:
140:
117:
87:J. H. van Lint
15:
9:
6:
4:
3:
2:
1246:
1235:
1232:
1230:
1227:
1225:
1222:
1221:
1219:
1208:
1203:
1201:
1196:
1194:
1189:
1188:
1182:
1180:
1176:
1172:
1167:
1164:
1160:
1159:
1155:
1144:
1141:
1139:
1136:
1134:
1133:
1128:
1122:
1121:
1118:
1112:
1109:
1107:
1104:
1102:
1101:Pseudoinverse
1099:
1097:
1094:
1092:
1089:
1087:
1084:
1082:
1079:
1077:
1074:
1073:
1071:
1069:Related terms
1067:
1061:
1060:Z (chemistry)
1058:
1056:
1053:
1051:
1048:
1046:
1043:
1041:
1038:
1036:
1033:
1031:
1028:
1026:
1023:
1021:
1018:
1016:
1013:
1011:
1008:
1006:
1003:
1001:
998:
997:
995:
991:
985:
982:
980:
977:
975:
972:
970:
967:
965:
962:
960:
957:
955:
952:
950:
947:
946:
944:
942:
937:
931:
928:
926:
923:
921:
918:
916:
913:
911:
908:
906:
903:
901:
898:
896:
893:
891:
888:
886:
883:
882:
880:
878:
873:
867:
864:
862:
859:
857:
854:
852:
849:
847:
844:
842:
839:
837:
834:
832:
829:
827:
824:
822:
819:
817:
814:
812:
809:
807:
804:
802:
799:
797:
794:
792:
789:
787:
784:
782:
779:
777:
774:
772:
769:
767:
764:
762:
759:
757:
754:
752:
749:
747:
744:
742:
739:
737:
734:
732:
729:
727:
724:
722:
719:
717:
714:
713:
711:
707:
701:
698:
696:
693:
691:
688:
686:
683:
681:
678:
676:
673:
671:
668:
666:
663:
661:
658:
656:
653:
651:
647:
644:
642:
639:
638:
636:
634:
630:
625:
619:
616:
614:
611:
609:
606:
604:
601:
599:
596:
594:
591:
589:
586:
584:
581:
580:
578:
576:
571:
565:
562:
560:
557:
555:
552:
550:
547:
545:
542:
540:
537:
535:
532:
530:
527:
525:
522:
520:
517:
516:
514:
510:
504:
501:
499:
496:
494:
491:
489:
486:
484:
481:
479:
476:
474:
471:
469:
466:
464:
461:
459:
456:
454:
451:
449:
446:
444:
441:
439:
436:
434:
431:
429:
426:
424:
421:
419:
418:Pentadiagonal
416:
414:
411:
409:
406:
404:
401:
399:
396:
394:
391:
389:
386:
384:
381:
379:
376:
374:
371:
369:
366:
364:
361:
359:
356:
354:
351:
349:
346:
344:
341:
339:
336:
334:
331:
329:
326:
324:
321:
319:
316:
314:
311:
309:
306:
304:
301:
299:
296:
294:
291:
289:
286:
284:
281:
279:
276:
274:
271:
269:
266:
264:
261:
259:
256:
254:
251:
249:
248:Anti-diagonal
246:
244:
241:
240:
238:
234:
229:
222:
217:
215:
210:
208:
203:
202:
199:
192:
188:
181:
177:
170:
167:
164:, vol. 28 (=
163:
159:
158:
152:
150:
145:
143:
136:
132:
128:
124:
120:
114:
110:
105:
101:
97:
92:
88:
83:
81:
77:
73:
68:
66:
62:
58:
54:
50:
46:
45:Seidel matrix
41:
37:
34:
30:
26:
22:
1179:expanding it
1171:graph theory
1168:
1153:
1123:
1055:Substitution
978:
941:graph theory
438:Quaternionic
428:Persymmetric
190:
180:D.G. Corneil
165:
161:
146:
138:
134:
126:
122:
115:
108:
106:
84:
79:
69:
64:
56:
48:
44:
35:
28:
25:graph theory
18:
1030:Hamiltonian
954:Biadjacency
890:Correlation
806:Householder
756:Commutation
493:Vandermonde
488:Tridiagonal
423:Permutation
413:Nonnegative
398:Matrix unit
278:Bisymmetric
193:1, 281–298.
94: [
76:eigenvalues
21:mathematics
1218:Categories
930:Transition
925:Stochastic
895:Covariance
877:statistics
856:Symplectic
851:Similarity
680:Unimodular
675:Orthogonal
660:Involutory
655:Invertible
650:Projection
646:Idempotent
588:Convergent
483:Triangular
433:Polynomial
378:Hessenberg
348:Equivalent
343:Elementary
323:Copositive
313:Conference
273:Bidiagonal
155:References
61:complement
1111:Wronskian
1035:Irregular
1025:Gell-Mann
974:Laplacian
969:Incidence
949:Adjacency
920:Precision
885:Centering
791:Generator
761:Confusion
746:Circulant
726:Augmented
685:Unipotent
665:Nilpotent
641:Congruent
618:Stieltjes
593:Defective
583:Companion
554:Redheffer
473:Symmetric
468:Sylvester
443:Signature
373:Hermitian
353:Frobenius
263:Arrowhead
243:Alternant
131:two-graph
1229:Matrices
939:Used in
875:Used in
836:Rotation
811:Jacobian
771:Distance
751:Cofactor
736:Carleman
716:Adjugate
700:Weighing
633:inverses
629:products
598:Definite
529:Identity
519:Exchange
512:Constant
478:Toeplitz
363:Hadamard
333:Diagonal
72:multiset
1040:Overlap
1005:Density
964:Edmonds
841:Seifert
801:Hessian
766:Coxeter
690:Unitary
608:Hurwitz
539:Of ones
524:Hilbert
458:Skyline
403:Metzler
393:Logical
388:Integer
298:Boolean
230:classes
959:Degree
900:Design
831:Random
821:Payoff
816:Moment
741:Cartan
731:Bézout
670:Normal
544:Pascal
534:Lehmer
463:Sparse
383:Hollow
368:Hankel
303:Cauchy
228:Matrix
27:, the
1169:This
1020:Gamma
984:Tutte
846:Shear
559:Shift
549:Pauli
498:Walsh
408:Moore
288:Block
102:]
38:is a
31:of a
23:, in
1175:stub
826:Pick
796:Gram
564:Zero
268:Band
137:and
89:and
70:The
915:Hat
648:or
631:or
82:.
74:of
63:of
55:of
19:In
1220::
151:.
144:.
100:nl
98:;
96:de
67:.
1206:e
1199:t
1192:v
1181:.
1045:S
503:Z
220:e
213:t
206:v
141:G
139:K
135:G
127:G
123:G
118:G
116:K
109:G
65:G
57:G
36:G
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.