Matrices with entries from the set {-1, 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
A002416
A272661
1x1
2
2
2
2
1
2x2
16
6
8
14
2
3x3
512
32
39
424
3
4x4
65,536
333
369
54,966
8
5x5
33,554,432
8,927
9,391
28,957,764
20
6x6
68,719,476,736
758,878
45
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
1x1
2
2
0
2
2x2
6
6
0
8
3x3
46
28
18
40
4x4
664
370
294
384
5x5
28,129
13,403
14,726
9,502
6x6
3,522,087
1,535,679
1,986,408
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
A046747
A055165
A060867
1x1
1
1
1
2x2
10
6
9
6
3x3
338
174
49
288
4x4
42,976
22,560
225
6,750
36,000
22,560
5x5
21,040,112
12,514,320
961
118,800
3,159,750
17,760,600
12,514,320
6x6
39,882,864,736
28,836,612,000
Determinant
Matrix Size
Number of Distinct Determinants
Maximum Determinant
Number of Unimodular Matrices
OEIS
A089472
A003432
1x1
2
1
1
2x2
3
1
6
3x3
5
2
168
4x4
7
3
20,040
5x5
11
5
9,702,720
6x6
19
9
18,480,102,480
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
3
3x3
25
4x4
543
5x5
29,281
6x6
3,781,503