Matrices with entries from the set {0, +1, +2} and diagonal entries fixed at 0.
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
A053764
2x2
9
4
5
8
4
3x3
729
42
45
690
16
4x4
531,441
2,329
2,372
515,970
64
5x5
3,486,784,401
871,436
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
2x2
7
7
0
5
3x3
98
62
36
45
4x4
8,141
4,629
3,512
2,373
5x5
4,190,019
2,064,975
2,125,044
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
2x2
5
4
4
4
3x3
361
368
36
324
368
4x4
198,736
332,705
220
12,904
185,611
332,705
5x5
907,245,701
2,579,538,700
Determinant
Matrix Size
Number of Distinct Determinants
Maximum Determinant
Number of Unimodular Matrices
OEIS
2x2
4
4
1
3x3
12
16
38
4x4
48
48
18,537
5x5
200
160
74,446,524
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
2x2
5
3x3
109
4x4
9,449
5x5
3,068,281