matrix-type
stringclasses 2
values | matrix-shape
stringclasses 20
values | Matrix Dimension
int64 1
9
| Number of Matrices
int64 2
847B
| Number of Characteristic Polynomials
int64 2
1.28B
| Number of Minimal Polynomials
int64 2
162k
⌀ | Number of Non-Derogatory Matrices
int64 2
42.3M
⌀ | Maximum Characteristic Height
int64 1
416
| Number of Distinct Eigenvalues
int64 2
23.8M
⌀ | Number of Distinct Real Eigenvalues
int64 1
6.65M
⌀ | Number of Distinct Purely Complex Eigenvalues
int64 0
17.1M
⌀ | Number of Distinct Jordan Canonical Forms
int64 2
162k
⌀ | Number of Singular Matrices
int64 0
238B
| Number of Non-Singular Matrices
int64 1
672B
| Number of Rank 1 Matrices
int64 0
3.2k
⌀ | Number of Rank 2 Matrices
int64 0
612k
⌀ | Number of Rank 3 Matrices
int64 0
14.5M
⌀ | Number of Rank 4 Matrices
int64 0
30.8M
⌀ | Number of Rank 5 Matrices
int64 0
12.5M
⌀ | Number of Rank 6 Matrices
int64 18.7k
11.7M
⌀ | Number of Distinct Determinants
int64 2
247
| Maximum Determinant
int64 1
160
| Number of Normal Matrices
int64 | Number of Rhapsodic Matrices
int64 | Number of Nilpotent Matrices
int64 0
244M
| Number of Unimodular Matrices
int64 0
130B
| Number of Totally Unimodular Matrices
int64 | Number of Type I Stable Matrices
int64 | Number of Type II Stable Matrices
int64 | Number of Rank 7 Matrices
int64 1.27M
1.81M
⌀ | Number of Rank 8 Matrices
int64 | Number of Rank 9 Matrices
int64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
upper-hessenberg
|
1_subdiag_0_1
| 2
| 8
| 6
| 6
| 8
| 2
| 6
| 6
| 0
| 6
| 4
| 4
| 4
| 4
| null | null | null | null | 2
| 1
| null | null | 1
| 4
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_0_1
| 3
| 64
| 28
| 28
| 64
| 3
| 43
| 25
| 18
| 28
| 30
| 34
| 0
| 30
| 34
| null | null | null | 5
| 2
| null | null | 1
| 32
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_0_1
| 4
| 1,024
| 197
| 197
| 1,024
| 6
| 413
| 219
| 194
| 197
| 440
| 584
| 0
| 0
| 440
| 584
| null | null | 7
| 3
| null | null | 1
| 508
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_0_1
| 5
| 32,768
| 2,235
| 2,235
| 32,768
| 13
| 6,920
| 3,264
| 3,656
| 2,235
| 12,792
| 19,976
| 0
| 0
| 0
| 12,792
| 19,976
| null | 11
| 5
| null | null | 1
| 15,944
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_0_1
| 6
| 2,097,152
| 39,768
| 39,768
| 2,097,152
| 27
| 166,005
| 75,045
| 90,960
| 39,768
| 740,732
| 1,356,420
| 0
| 0
| 0
| 0
| 740,732
| 1,356,420
| 17
| 8
| null | null | 1
| 988,836
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_0_1
| 7
| 268,435,456
| 1,140,848
| null | null | 55
| 6,176,985
| 2,694,199
| 3,482,786
| null | 85,591,032
| 182,844,424
| null | null | null | null | null | null | 27
| 13
| null | null | 1
| 121,294,672
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_0_1
| 8
| 68,719,476,736
| 51,925,106
| null | null | 120
| null | null | null | null | 19,751,265,584
| 48,968,211,152
| null | null | null | null | null | null | 43
| 21
| null | null | 1
| 29,467,080,660
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_0_diag_n1_0_1
| 2
| 3
| 3
| 3
| 3
| 1
| 5
| 3
| 2
| 3
| 1
| 2
| 1
| 2
| null | null | null | null | 3
| 1
| null | null | 1
| 2
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_0_diag_n1_0_1
| 3
| 27
| 15
| 15
| 27
| 2
| 35
| 15
| 20
| 15
| 9
| 18
| 0
| 9
| 18
| null | null | null | 3
| 1
| null | null | 3
| 18
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_0_diag_n1_0_1
| 4
| 729
| 140
| 140
| 729
| 4
| 431
| 135
| 296
| 140
| 243
| 486
| 0
| 0
| 243
| 486
| null | null | 5
| 2
| null | null | 21
| 378
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_0_diag_n1_0_1
| 5
| 59,049
| 2,297
| 2,297
| 59,049
| 5
| 9,497
| 2,877
| 6,620
| 2,297
| 17,739
| 41,310
| 0
| 0
| 0
| 17,739
| 41,310
| null | 7
| 3
| null | null | 271
| 27,702
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_0_diag_n1_0_1
| 6
| 14,348,907
| 67,628
| 67,628
| 14,348,907
| 9
| 363,143
| 103,987
| 259,156
| 67,628
| 3,733,209
| 10,615,698
| 0
| 0
| 0
| 0
| 3,733,209
| 10,615,698
| 11
| 5
| null | null | 9,075
| 6,075,486
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_0_diag_n1_0_1
| 7
| 10,460,353,203
| 3,606,225
| null | null | 15
| 23,795,195
| 6,648,959
| 17,146,236
| null | 2,334,620,313
| 8,125,732,890
| null | null | null | null | null | null | 17
| 8
| null | null | 685,033
| 3,965,691,474
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_n1_0_1
| 2
| 27
| 16
| 16
| 27
| 2
| 21
| 11
| 10
| 16
| 9
| 18
| 9
| 8
| null | null | null | null | 5
| 2
| null | null | 3
| 14
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_n1_0_1
| 3
| 729
| 166
| 166
| 729
| 5
| 307
| 127
| 180
| 166
| 211
| 518
| 0
| 211
| 518
| null | null | null | 9
| 4
| null | null | 15
| 326
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_n1_0_1
| 4
| 59,049
| 3,317
| 3,317
| 59,049
| 12
| 9,235
| 3,229
| 6,006
| 3,317
| 14,307
| 44,742
| 0
| 0
| 14,307
| 44,742
| null | null | 17
| 8
| null | null | 163
| 23,162
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_n1_0_1
| 5
| 14,348,907
| 133,255
| 133,255
| 14,348,907
| 28
| 535,375
| 180,603
| 354,772
| 133,255
| 2,881,977
| 11,466,930
| 0
| 0
| 0
| 2,881,977
| 11,466,930
| null | 33
| 16
| null | null | 4,389
| 4,900,146
| null | null | null | null | null | null |
upper-hessenberg
|
1_subdiag_n1_0_1
| 6
| 10,460,353,203
| 10,872,459
| null | null | 66
| null | null | null | null | 1,737,616,657
| 8,722,736,546
| null | null | null | null | null | null | 65
| 32
| null | null | 272,867
| 3,075,388,478
| null | null | null | null | null | null |
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