Matrices with entries from the set {0, +1, +2}.
Characteristic Polynomials
Data files have been temporarily removed due to unexpected costs, if you would like access to the characteristic polynomial data files please contact me at sthornt7@uwo.ca .
Download all characteristic polynomials:
Minimal Polynomials
Download all minimal polynomials:
Properties
Download all properties: Properties.csv
Characteristic Polynomials
Matrix Size
Number of Matrices
Number of Characteristic Polynomials
Number of Minimal Polynomials
Number of Non-Derogatory Matrices
Maximum Characteristic Height
OEIS
A060722
A272659
A306783
A306818
1x1
3
3
3
3
2
2x2
81
22
25
78
4
3x3
19,683
513
532
19,068
16
4x4
43,046,721
58,335
58,693
42,300,060
64
5x5
847,288,609,443
40,422,490
240
Eigenvalues
Matrix Size
Number of Distinct Eigenvalues
Number of Distinct Real Eigenvalues
Number of Distinct Purely Complex Eigenvalues
Number of Distinct Jordan Canonical Forms
OEIS
A306792
A306795
1x1
3
3
0
3
2x2
25
25
0
25
3x3
1,027
657
370
536
4x4
193,244
112,870
80,374
58,762
5x5
Rank
Matrix Size
Number of Singular Matrices
Number of Non-Singular Matrices
Number of Rank 1 Matrices
Number of Rank 2 Matrices
Number of Rank 3 Matrices
Number of Rank 4 Matrices
Number of Rank 5 Matrices
OEIS
A306840
A197487
1x1
1
2
2
2x2
31
50
50
30
3x3
6,891
12,792
266
6,624
12,792
4x4
12,202,161
30,844,560
1,950
388,946
11,811,264
30,844,560
5x5
175,419,087,483
671,869,521,960
Determinant
Matrix Size
Number of Distinct Determinants
Maximum Determinant
Number of Unimodular Matrices
OEIS
1x1
3
2
1
2x2
9
4
14
3x3
25
16
2,022
4x4
67
48
2,699,544
5x5
233
160
31,519,662,120
Miscellaneous
Matrix Size
Number of Normal Matrices
Number of Rhapsodic Matrices
Number of Nilpotent Matrices
Number of Totally Unimodular Matrices
Number of Type I Stable Matrices
Number of Type II Stable Matrices
OEIS
1x1
1
2x2
5
3x3
109
4x4
9,449
5x5
3,068,281