Matrices with entries from the set {-1, 0, +1} 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
3
4
8
1
3x3
729
20
22
684
3
4x4
531,441
381
404
506,472
9
5x5
3,486,784,401
38,145
25
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
5
3
2
4
3x3
43
17
26
22
4x4
1,161
363
798
405
5x5
170,935
52,981
117,954
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
393
336
36
356
356
4x4
236,833
294,608
232
16,728
219,872
294,608
5x5
1,234,304,529
2,252,479,872
Determinant
Matrix Size
Number of Distinct Determinants
Maximum Determinant
Number of Unimodular Matrices
OEIS
2x2
3
1
4
3x3
5
2
304
4x4
15
9
182,544
5x5
43
22
848,818,816
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
133
4x4
18,905
5x5
13,998,201