Matrices with entries from the set {-1, +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
A053763
2x2
4
2
2
4
1
3x3
64
6
6
56
3
4x4
4,096
27
32
3,328
9
5x5
1,048,576
222
260
830,912
25
6x6
1,073,741,824
5,091
125
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
4
2
2
2
3x3
11
5
6
6
4x4
60
20
40
32
5x5
635
169
466
260
6x6
21,686
5,652
16,034
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
Number of Rank 6 Matrices
OEIS
2x2
0
4
0
4
3x3
32
32
0
32
32
4x4
0
4,096
0
0
0
4,096
5x5
203,776
844,800
0
0
0
203,776
844,800
6x6
0
1,073,741,824
Determinant
Matrix Size
Number of Distinct Determinants
Maximum Determinant
Number of Unimodular Matrices
OEIS
2x2
2
1
4
3x3
3
2
0
4x4
8
9
1,920
5x5
19
22
0
6x6
74
125
146,227,200
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
0
3x3
0
4x4
0
5x5
0
6x6
0