Matrices with entries from the set {-1, 0, +1}.
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
A272658
A271587
A306817
1x1
3
3
3
3
1
2x2
81
16
19
78
2
3x3
19,683
209
220
18,942
6
4x4
43,046,721
8,739
8,924
41,840,168
16
5x5
847,288,609,443
1,839,102
80
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
A271570
A306002
1x1
3
3
0
3
2x2
21
11
10
19
3x3
375
157
218
225
4x4
24,823
8,825
15,998
8,971
5x5
7,963,249
2,681,903
5,281,346
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
A057981
A056989
A060868
1x1
1
2
2
2x2
33
48
32
48
3x3
7,875
11,808
338
7,536
11,808
4x4
15,099,201
27,947,520
3,200
611,520
14,484,480
27,947,520
5x5
237,634,987,683
609,653,621,760
Determinant
Matrix Size
Number of Distinct Determinants
Maximum Determinant
Number of Unimodular Matrices
OEIS
A306838
A306839
1x1
3
1
2
2x2
5
2
40
3x3
9
4
6,960
4x4
25
16
10,340,736
5x5
67
48
129,599,358,720
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
A306820
1x1
1
2x2
9
3x3
481
4x4
148,817
5x5
243,782,721