Bohemian Matrices

Unstructured_n1_0

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:

Matrix Size .csv .zip .tar.gz
1x1 CharPolys_1x1.csv (26B) CharPolys_1x1.zip (206B) CharPolys_1x1.tar.gz (156B)
2x2 CharPolys_2x2.csv (68B) CharPolys_2x2.zip (232B) CharPolys_2x2.tar.gz (177B)
3x3 CharPolys_3x3.csv (378B) CharPolys_3x3.zip (333B) CharPolys_3x3.tar.gz (288B)
4x4 CharPolys_4x4.csv (5KB) CharPolys_4x4.zip (1KB) CharPolys_4x4.tar.gz (1KB)
5x5 CharPolys_5x5.csv (158KB) CharPolys_5x5.zip (33KB) CharPolys_5x5.tar.gz (33KB)
6x6 CharPolys_6x6.csv (16MB) CharPolys_6x6.zip (3MB) CharPolys_6x6.tar.gz (3MB)

Minimal Polynomials

Download all minimal polynomials:

Matrix Size .csv .zip .tar.gz
1x1 MinPolys_1x1.csv (28B) MinPolys_1x1.zip (204B) MinPolys_1x1.tar.gz (155B)
2x2 MinPolys_2x2.csv (92B) MinPolys_2x2.zip (241B) MinPolys_2x2.tar.gz (184B)
3x3 MinPolys_3x3.csv (491B) MinPolys_3x3.zip (364B) MinPolys_3x3.tar.gz (322B)
4x4 MinPolys_4x4.csv (6KB) MinPolys_4x4.zip (2KB) MinPolys_4x4.tar.gz (2KB)
5x5 MinPolys_5x5.csv (175KB) MinPolys_5x5.zip (44KB) MinPolys_5x5.tar.gz (44KB)

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