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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