2153:
586:
890:
483:
752:
1071:
757:
1124:
955:
679:
581:{\displaystyle J={\begin{bmatrix}\lambda &1&\;&\;\\\;&\lambda &\ddots &\;\\\;&\;&\ddots &1\\\;&\;&\;&\lambda \end{bmatrix}},}
993:
1811:
475:
449:
423:
134:
67:
613:
319:
299:
275:
255:
178:
207:
425:
or larger (that is, not completely diagonal) is defective. (A diagonal matrix is a special case of the Jordan normal form with all trivial Jordan blocks of size
633:
363:
343:
235:
154:
94:
2025:
1244:
2116:
1213:
1191:
2035:
1801:
684:
160:, since distinct eigenvalues always have linearly independent eigenvectors. In particular, a defective matrix has one or more eigenvalues
1020:
885:{\displaystyle v_{2}={\begin{bmatrix}0\\1\\\vdots \\0\end{bmatrix}},~\ldots ,~v_{n}={\begin{bmatrix}0\\0\\\vdots \\1\end{bmatrix}}}
1836:
1383:
1183:
104:
1600:
1237:
1086:
1675:
1831:
1353:
895:
1935:
1806:
1720:
214:
2040:
1930:
1638:
1318:
2189:
2075:
2004:
1886:
1746:
1343:
1230:
100:
1945:
1528:
1333:
1003:
638:
635:(or greater if there are other Jordan blocks with the same eigenvalue), but only one distinct eigenvector
278:
181:
32:
1891:
1628:
1478:
1473:
1308:
1283:
1278:
40:
2152:
2085:
1443:
1273:
1253:
210:
96:
69:
2106:
2080:
1658:
1463:
1453:
960:
2157:
2111:
2101:
2055:
2050:
1979:
1915:
1781:
1518:
1513:
1448:
1438:
1303:
1138:
999:
454:
428:
402:
113:
46:
2194:
2168:
1955:
1950:
1940:
1920:
1881:
1876:
1705:
1700:
1685:
1680:
1671:
1666:
1613:
1508:
1458:
1403:
1373:
1368:
1348:
1338:
1298:
1209:
1187:
598:
304:
284:
260:
240:
163:
2163:
2131:
2060:
1999:
1994:
1974:
1910:
1816:
1786:
1771:
1756:
1751:
1690:
1643:
1608:
1579:
1498:
1493:
1468:
1398:
1378:
1288:
1268:
376:
372:
186:
1861:
1796:
1776:
1761:
1741:
1725:
1623:
1554:
1544:
1503:
1388:
1358:
2121:
2065:
2045:
2030:
1989:
1866:
1826:
1791:
1715:
1654:
1633:
1574:
1564:
1549:
1483:
1428:
1418:
1413:
1323:
618:
380:
348:
328:
220:
139:
79:
73:
20:
1141: – Form of a matrix indicating its eigenvalues and their algebraic multiplicities
2183:
2126:
1984:
1925:
1856:
1846:
1841:
1766:
1695:
1569:
1559:
1488:
1408:
1393:
1328:
1202:
396:
387:(which includes Hermitian and unitary matrices as special cases) is never defective.
384:
28:
2009:
1966:
1871:
1584:
1523:
1433:
1313:
1851:
1821:
1589:
1423:
1293:
369:
36:
1902:
1363:
1077:
592:
157:
99:
eigenvectors. A complete basis is formed by augmenting the eigenvectors with
2136:
1710:
281:(that is, the number of linearly independent eigenvectors associated with
2070:
747:{\displaystyle v_{1}={\begin{bmatrix}1\\0\\\vdots \\0\end{bmatrix}}.}
1222:
1226:
1066:{\displaystyle {\begin{bmatrix}3&1\\0&3\end{bmatrix}},}
16:
Non-diagonalizable matrix; one lacking a basis of eigenvectors
325:. However, every eigenvalue with algebraic multiplicity
103:, which are necessary for solving defective systems of
1095:
1029:
847:
779:
706:
498:
1089:
1023:
963:
898:
760:
687:
641:
621:
601:
486:
457:
431:
405:
351:
331:
307:
287:
263:
243:
223:
189:
166:
142:
116:
82:
49:
2094:
2018:
1964:
1900:
1734:
1652:
1598:
1537:
1261:
892:form a chain of generalized eigenvectors such that
1201:
1119:{\displaystyle {\begin{bmatrix}1\\0\end{bmatrix}}}
1118:
1065:
987:
949:
884:
746:
673:
627:
607:
580:
469:
443:
417:
357:
337:
313:
293:
269:
249:
237:linearly independent eigenvectors associated with
229:
201:
172:
148:
128:
88:
61:
365:linearly independent generalized eigenvectors.
1238:
1178:Golub, Gene H.; Van Loan, Charles F. (1996),
1161:
8:
950:{\displaystyle Jv_{k}=\lambda v_{k}+v_{k-1}}
1812:Fundamental (linear differential equation)
1245:
1231:
1223:
1014:A simple example of a defective matrix is
561:
558:
555:
540:
537:
532:
519:
514:
511:
1090:
1088:
1024:
1022:
962:
935:
922:
906:
897:
842:
833:
774:
765:
759:
701:
692:
686:
665:
649:
640:
620:
600:
493:
485:
456:
430:
404:
350:
330:
306:
286:
262:
242:
222:
188:
165:
141:
115:
81:
48:
451:and is not defective.) For example, the
383:, is never defective; more generally, a
2117:Matrix representation of conic sections
1157:
1155:
1151:
1080:of 3 but only one distinct eigenvector
1002:, which is as close as one can come to
136:defective matrix always has fewer than
998:Any defective matrix has a nontrivial
1208:(3rd ed.). San Diego: Harcourt.
7:
674:{\displaystyle Jv_{1}=\lambda v_{1}}
1204:Linear Algebra and Its Applications
257:. If the algebraic multiplicity of
1129:(and constant multiples thereof).
754:The other canonical basis vectors
14:
2151:
2019:Used in science and engineering
105:ordinary differential equations
1262:Explicitly constrained entries
1184:Johns Hopkins University Press
31:that does not have a complete
1:
2036:Fundamental (computer vision)
988:{\displaystyle k=2,\ldots ,n}
615:with algebraic multiplicity
209:(that is, they are multiple
1802:Duplication and elimination
1601:eigenvalues or eigenvectors
1182:(3rd ed.), Baltimore:
2211:
1735:With specific applications
1364:Discrete Fourier Transform
1162:Golub & Van Loan (1996
2145:
2026:Cabibbo–Kobayashi–Maskawa
1653:Satisfying conditions on
470:{\displaystyle n\times n}
444:{\displaystyle 1\times 1}
418:{\displaystyle 2\times 2}
215:characteristic polynomial
129:{\displaystyle n\times n}
62:{\displaystyle n\times n}
1200:Strang, Gilbert (1988).
608:{\displaystyle \lambda }
314:{\displaystyle \lambda }
294:{\displaystyle \lambda }
270:{\displaystyle \lambda }
250:{\displaystyle \lambda }
173:{\displaystyle \lambda }
101:generalized eigenvectors
1384:Generalized permutation
39:, and is therefore not
2158:Mathematics portal
1120:
1067:
989:
951:
886:
748:
675:
629:
609:
582:
471:
445:
419:
359:
339:
315:
295:
279:geometric multiplicity
271:
251:
231:
203:
202:{\displaystyle m>1}
182:algebraic multiplicity
174:
150:
130:
90:
63:
1121:
1068:
990:
952:
887:
749:
676:
630:
610:
583:
472:
446:
420:
375:and more generally a
360:
340:
316:
296:
272:
252:
232:
204:
175:
151:
131:
91:
64:
1087:
1021:
961:
896:
758:
685:
639:
619:
599:
484:
455:
429:
403:
349:
329:
323:defective eigenvalue
305:
285:
261:
241:
221:
187:
164:
140:
114:
107:and other problems.
97:linearly independent
80:
47:
43:. In particular, an
2107:Linear independence
1354:Diagonally dominant
1180:Matrix Computations
1076:which has a double
2112:Matrix exponential
2102:Jordan normal form
1936:Fisher information
1807:Euclidean distance
1721:Totally unimodular
1139:Jordan normal form
1116:
1110:
1063:
1054:
1006:of such a matrix.
1000:Jordan normal form
985:
947:
882:
876:
808:
744:
735:
671:
625:
605:
578:
569:
467:
441:
415:
355:
335:
311:
291:
267:
247:
227:
217:), but fewer than
199:
170:
146:
126:
86:
59:
2177:
2176:
2169:Category:Matrices
2041:Fuzzy associative
1931:Doubly stochastic
1639:Positive-definite
1319:Block tridiagonal
1215:978-970-686-609-7
1193:978-0-8018-5414-9
828:
819:
628:{\displaystyle n}
358:{\displaystyle m}
338:{\displaystyle m}
230:{\displaystyle m}
149:{\displaystyle n}
89:{\displaystyle n}
76:it does not have
2202:
2164:List of matrices
2156:
2155:
2132:Row echelon form
2076:State transition
2005:Seidel adjacency
1887:Totally positive
1747:Alternating sign
1344:Complex Hadamard
1247:
1240:
1233:
1224:
1219:
1207:
1196:
1165:
1159:
1125:
1123:
1122:
1117:
1115:
1114:
1072:
1070:
1069:
1064:
1059:
1058:
994:
992:
991:
986:
956:
954:
953:
948:
946:
945:
927:
926:
911:
910:
891:
889:
888:
883:
881:
880:
838:
837:
826:
817:
813:
812:
770:
769:
753:
751:
750:
745:
740:
739:
697:
696:
680:
678:
677:
672:
670:
669:
654:
653:
634:
632:
631:
626:
614:
612:
611:
606:
587:
585:
584:
579:
574:
573:
476:
474:
473:
468:
450:
448:
447:
442:
424:
422:
421:
416:
377:Hermitian matrix
373:symmetric matrix
364:
362:
361:
356:
344:
342:
341:
336:
321:is said to be a
320:
318:
317:
312:
300:
298:
297:
292:
276:
274:
273:
268:
256:
254:
253:
248:
236:
234:
233:
228:
208:
206:
205:
200:
179:
177:
176:
171:
155:
153:
152:
147:
135:
133:
132:
127:
95:
93:
92:
87:
68:
66:
65:
60:
25:defective matrix
2210:
2209:
2205:
2204:
2203:
2201:
2200:
2199:
2180:
2179:
2178:
2173:
2150:
2141:
2090:
2014:
1960:
1896:
1730:
1648:
1594:
1533:
1334:Centrosymmetric
1257:
1251:
1216:
1199:
1194:
1177:
1174:
1169:
1168:
1160:
1153:
1148:
1135:
1109:
1108:
1102:
1101:
1091:
1085:
1084:
1053:
1052:
1047:
1041:
1040:
1035:
1025:
1019:
1018:
1012:
1004:diagonalization
959:
958:
931:
918:
902:
894:
893:
875:
874:
868:
867:
861:
860:
854:
853:
843:
829:
807:
806:
800:
799:
793:
792:
786:
785:
775:
761:
756:
755:
734:
733:
727:
726:
720:
719:
713:
712:
702:
688:
683:
682:
661:
645:
637:
636:
617:
616:
597:
596:
568:
567:
562:
559:
556:
552:
551:
546:
541:
538:
534:
533:
530:
525:
520:
516:
515:
512:
509:
504:
494:
482:
481:
453:
452:
427:
426:
401:
400:
395:Any nontrivial
393:
347:
346:
327:
326:
303:
302:
283:
282:
259:
258:
239:
238:
219:
218:
185:
184:
162:
161:
138:
137:
112:
111:
78:
77:
45:
44:
17:
12:
11:
5:
2208:
2206:
2198:
2197:
2192:
2190:Linear algebra
2182:
2181:
2175:
2174:
2172:
2171:
2166:
2161:
2146:
2143:
2142:
2140:
2139:
2134:
2129:
2124:
2122:Perfect matrix
2119:
2114:
2109:
2104:
2098:
2096:
2092:
2091:
2089:
2088:
2083:
2078:
2073:
2068:
2063:
2058:
2053:
2048:
2043:
2038:
2033:
2028:
2022:
2020:
2016:
2015:
2013:
2012:
2007:
2002:
1997:
1992:
1987:
1982:
1977:
1971:
1969:
1962:
1961:
1959:
1958:
1953:
1948:
1943:
1938:
1933:
1928:
1923:
1918:
1913:
1907:
1905:
1898:
1897:
1895:
1894:
1892:Transformation
1889:
1884:
1879:
1874:
1869:
1864:
1859:
1854:
1849:
1844:
1839:
1834:
1829:
1824:
1819:
1814:
1809:
1804:
1799:
1794:
1789:
1784:
1779:
1774:
1769:
1764:
1759:
1754:
1749:
1744:
1738:
1736:
1732:
1731:
1729:
1728:
1723:
1718:
1713:
1708:
1703:
1698:
1693:
1688:
1683:
1678:
1669:
1663:
1661:
1650:
1649:
1647:
1646:
1641:
1636:
1631:
1629:Diagonalizable
1626:
1621:
1616:
1611:
1605:
1603:
1599:Conditions on
1596:
1595:
1593:
1592:
1587:
1582:
1577:
1572:
1567:
1562:
1557:
1552:
1547:
1541:
1539:
1535:
1534:
1532:
1531:
1526:
1521:
1516:
1511:
1506:
1501:
1496:
1491:
1486:
1481:
1479:Skew-symmetric
1476:
1474:Skew-Hermitian
1471:
1466:
1461:
1456:
1451:
1446:
1441:
1436:
1431:
1426:
1421:
1416:
1411:
1406:
1401:
1396:
1391:
1386:
1381:
1376:
1371:
1366:
1361:
1356:
1351:
1346:
1341:
1336:
1331:
1326:
1321:
1316:
1311:
1309:Block-diagonal
1306:
1301:
1296:
1291:
1286:
1284:Anti-symmetric
1281:
1279:Anti-Hermitian
1276:
1271:
1265:
1263:
1259:
1258:
1252:
1250:
1249:
1242:
1235:
1227:
1221:
1220:
1214:
1197:
1192:
1173:
1170:
1167:
1166:
1164:, p. 316)
1150:
1149:
1147:
1144:
1143:
1142:
1134:
1131:
1127:
1126:
1113:
1107:
1104:
1103:
1100:
1097:
1096:
1094:
1074:
1073:
1062:
1057:
1051:
1048:
1046:
1043:
1042:
1039:
1036:
1034:
1031:
1030:
1028:
1011:
1008:
984:
981:
978:
975:
972:
969:
966:
944:
941:
938:
934:
930:
925:
921:
917:
914:
909:
905:
901:
879:
873:
870:
869:
866:
863:
862:
859:
856:
855:
852:
849:
848:
846:
841:
836:
832:
825:
822:
816:
811:
805:
802:
801:
798:
795:
794:
791:
788:
787:
784:
781:
780:
778:
773:
768:
764:
743:
738:
732:
729:
728:
725:
722:
721:
718:
715:
714:
711:
708:
707:
705:
700:
695:
691:
668:
664:
660:
657:
652:
648:
644:
624:
604:
589:
588:
577:
572:
566:
563:
560:
557:
554:
553:
550:
547:
545:
542:
539:
536:
535:
531:
529:
526:
524:
521:
518:
517:
513:
510:
508:
505:
503:
500:
499:
497:
492:
489:
466:
463:
460:
440:
437:
434:
414:
411:
408:
392:
389:
381:unitary matrix
354:
334:
310:
290:
266:
246:
226:
198:
195:
192:
169:
145:
125:
122:
119:
85:
74:if and only if
58:
55:
52:
41:diagonalizable
21:linear algebra
15:
13:
10:
9:
6:
4:
3:
2:
2207:
2196:
2193:
2191:
2188:
2187:
2185:
2170:
2167:
2165:
2162:
2160:
2159:
2154:
2148:
2147:
2144:
2138:
2135:
2133:
2130:
2128:
2127:Pseudoinverse
2125:
2123:
2120:
2118:
2115:
2113:
2110:
2108:
2105:
2103:
2100:
2099:
2097:
2095:Related terms
2093:
2087:
2086:Z (chemistry)
2084:
2082:
2079:
2077:
2074:
2072:
2069:
2067:
2064:
2062:
2059:
2057:
2054:
2052:
2049:
2047:
2044:
2042:
2039:
2037:
2034:
2032:
2029:
2027:
2024:
2023:
2021:
2017:
2011:
2008:
2006:
2003:
2001:
1998:
1996:
1993:
1991:
1988:
1986:
1983:
1981:
1978:
1976:
1973:
1972:
1970:
1968:
1963:
1957:
1954:
1952:
1949:
1947:
1944:
1942:
1939:
1937:
1934:
1932:
1929:
1927:
1924:
1922:
1919:
1917:
1914:
1912:
1909:
1908:
1906:
1904:
1899:
1893:
1890:
1888:
1885:
1883:
1880:
1878:
1875:
1873:
1870:
1868:
1865:
1863:
1860:
1858:
1855:
1853:
1850:
1848:
1845:
1843:
1840:
1838:
1835:
1833:
1830:
1828:
1825:
1823:
1820:
1818:
1815:
1813:
1810:
1808:
1805:
1803:
1800:
1798:
1795:
1793:
1790:
1788:
1785:
1783:
1780:
1778:
1775:
1773:
1770:
1768:
1765:
1763:
1760:
1758:
1755:
1753:
1750:
1748:
1745:
1743:
1740:
1739:
1737:
1733:
1727:
1724:
1722:
1719:
1717:
1714:
1712:
1709:
1707:
1704:
1702:
1699:
1697:
1694:
1692:
1689:
1687:
1684:
1682:
1679:
1677:
1673:
1670:
1668:
1665:
1664:
1662:
1660:
1656:
1651:
1645:
1642:
1640:
1637:
1635:
1632:
1630:
1627:
1625:
1622:
1620:
1617:
1615:
1612:
1610:
1607:
1606:
1604:
1602:
1597:
1591:
1588:
1586:
1583:
1581:
1578:
1576:
1573:
1571:
1568:
1566:
1563:
1561:
1558:
1556:
1553:
1551:
1548:
1546:
1543:
1542:
1540:
1536:
1530:
1527:
1525:
1522:
1520:
1517:
1515:
1512:
1510:
1507:
1505:
1502:
1500:
1497:
1495:
1492:
1490:
1487:
1485:
1482:
1480:
1477:
1475:
1472:
1470:
1467:
1465:
1462:
1460:
1457:
1455:
1452:
1450:
1447:
1445:
1444:Pentadiagonal
1442:
1440:
1437:
1435:
1432:
1430:
1427:
1425:
1422:
1420:
1417:
1415:
1412:
1410:
1407:
1405:
1402:
1400:
1397:
1395:
1392:
1390:
1387:
1385:
1382:
1380:
1377:
1375:
1372:
1370:
1367:
1365:
1362:
1360:
1357:
1355:
1352:
1350:
1347:
1345:
1342:
1340:
1337:
1335:
1332:
1330:
1327:
1325:
1322:
1320:
1317:
1315:
1312:
1310:
1307:
1305:
1302:
1300:
1297:
1295:
1292:
1290:
1287:
1285:
1282:
1280:
1277:
1275:
1274:Anti-diagonal
1272:
1270:
1267:
1266:
1264:
1260:
1255:
1248:
1243:
1241:
1236:
1234:
1229:
1228:
1225:
1217:
1211:
1206:
1205:
1198:
1195:
1189:
1185:
1181:
1176:
1175:
1171:
1163:
1158:
1156:
1152:
1145:
1140:
1137:
1136:
1132:
1130:
1111:
1105:
1098:
1092:
1083:
1082:
1081:
1079:
1060:
1055:
1049:
1044:
1037:
1032:
1026:
1017:
1016:
1015:
1009:
1007:
1005:
1001:
996:
982:
979:
976:
973:
970:
967:
964:
942:
939:
936:
932:
928:
923:
919:
915:
912:
907:
903:
899:
877:
871:
864:
857:
850:
844:
839:
834:
830:
823:
820:
814:
809:
803:
796:
789:
782:
776:
771:
766:
762:
741:
736:
730:
723:
716:
709:
703:
698:
693:
689:
666:
662:
658:
655:
650:
646:
642:
622:
602:
594:
575:
570:
564:
548:
543:
527:
522:
506:
501:
495:
490:
487:
480:
479:
478:
477:Jordan block
464:
461:
458:
438:
435:
432:
412:
409:
406:
398:
390:
388:
386:
385:normal matrix
382:
378:
374:
371:
366:
352:
332:
324:
308:
288:
280:
264:
244:
224:
216:
212:
196:
193:
190:
183:
167:
159:
143:
123:
120:
117:
108:
106:
102:
98:
83:
75:
72:is defective
71:
56:
53:
50:
42:
38:
34:
30:
29:square matrix
26:
22:
2149:
2081:Substitution
1967:graph theory
1618:
1464:Quaternionic
1454:Persymmetric
1203:
1179:
1128:
1075:
1013:
997:
590:
397:Jordan block
394:
391:Jordan block
367:
322:
277:exceeds its
109:
37:eigenvectors
24:
18:
2056:Hamiltonian
1980:Biadjacency
1916:Correlation
1832:Householder
1782:Commutation
1519:Vandermonde
1514:Tridiagonal
1449:Permutation
1439:Nonnegative
1424:Matrix unit
1304:Bisymmetric
345:always has
158:eigenvalues
2184:Categories
1956:Transition
1951:Stochastic
1921:Covariance
1903:statistics
1882:Symplectic
1877:Similarity
1706:Unimodular
1701:Orthogonal
1686:Involutory
1681:Invertible
1676:Projection
1672:Idempotent
1614:Convergent
1509:Triangular
1459:Polynomial
1404:Hessenberg
1374:Equivalent
1369:Elementary
1349:Copositive
1339:Conference
1299:Bidiagonal
1172:References
1078:eigenvalue
593:eigenvalue
2137:Wronskian
2061:Irregular
2051:Gell-Mann
2000:Laplacian
1995:Incidence
1975:Adjacency
1946:Precision
1911:Centering
1817:Generator
1787:Confusion
1772:Circulant
1752:Augmented
1711:Unipotent
1691:Nilpotent
1667:Congruent
1644:Stieltjes
1619:Defective
1609:Companion
1580:Redheffer
1499:Symmetric
1494:Sylvester
1469:Signature
1399:Hermitian
1379:Frobenius
1289:Arrowhead
1269:Alternant
977:…
940:−
916:λ
865:⋮
821:…
797:⋮
724:⋮
659:λ
603:λ
565:λ
544:⋱
528:⋱
523:λ
502:λ
462:×
436:×
410:×
309:λ
289:λ
265:λ
245:λ
168:λ
156:distinct
121:×
54:×
2195:Matrices
1965:Used in
1901:Used in
1862:Rotation
1837:Jacobian
1797:Distance
1777:Cofactor
1762:Carleman
1742:Adjugate
1726:Weighing
1659:inverses
1655:products
1624:Definite
1555:Identity
1545:Exchange
1538:Constant
1504:Toeplitz
1389:Hadamard
1359:Diagonal
1133:See also
681:, where
399:of size
379:, and a
301:), then
2066:Overlap
2031:Density
1990:Edmonds
1867:Seifert
1827:Hessian
1792:Coxeter
1716:Unitary
1634:Hurwitz
1565:Of ones
1550:Hilbert
1484:Skyline
1429:Metzler
1419:Logical
1414:Integer
1324:Boolean
1256:classes
1010:Example
591:has an
213:of the
1985:Degree
1926:Design
1857:Random
1847:Payoff
1842:Moment
1767:Cartan
1757:BĂ©zout
1696:Normal
1570:Pascal
1560:Lehmer
1489:Sparse
1409:Hollow
1394:Hankel
1329:Cauchy
1254:Matrix
1212:
1190:
827:
818:
70:matrix
2046:Gamma
2010:Tutte
1872:Shear
1585:Shift
1575:Pauli
1524:Walsh
1434:Moore
1314:Block
1146:Notes
211:roots
180:with
33:basis
27:is a
1852:Pick
1822:Gram
1590:Zero
1294:Band
1210:ISBN
1188:ISBN
957:for
370:real
194:>
23:, a
1941:Hat
1674:or
1657:or
110:An
35:of
19:In
2186::
1186:,
1154:^
995:.
595:,
368:A
2071:S
1529:Z
1246:e
1239:t
1232:v
1218:.
1112:]
1106:0
1099:1
1093:[
1061:,
1056:]
1050:3
1045:0
1038:1
1033:3
1027:[
983:n
980:,
974:,
971:2
968:=
965:k
943:1
937:k
933:v
929:+
924:k
920:v
913:=
908:k
904:v
900:J
878:]
872:1
858:0
851:0
845:[
840:=
835:n
831:v
824:,
815:,
810:]
804:0
790:1
783:0
777:[
772:=
767:2
763:v
742:.
737:]
731:0
717:0
710:1
704:[
699:=
694:1
690:v
667:1
663:v
656:=
651:1
647:v
643:J
623:n
576:,
571:]
549:1
507:1
496:[
491:=
488:J
465:n
459:n
439:1
433:1
413:2
407:2
353:m
333:m
225:m
197:1
191:m
144:n
124:n
118:n
84:n
57:n
51:n
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