Bohemian Matrices

Unstructured_n1_0_1

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:

Matrix Size .csv .zip .tar.gz
1x1 CharPolys_1x1.csv (33B) CharPolys_1x1.zip (210B) CharPolys_1x1.tar.gz (159B)
2x2 CharPolys_2x2.csv (159B) CharPolys_2x2.zip (264B) CharPolys_2x2.tar.gz (212B)
3x3 CharPolys_3x3.csv (3KB) CharPolys_3x3.zip (874B) CharPolys_3x3.tar.gz (846B)
4x4 CharPolys_4x4.csv (139KB) CharPolys_4x4.zip (31KB) CharPolys_4x4.tar.gz (31KB)
5x5 CharPolys_5x5.csv (37MB) CharPolys_5x5.zip (7MB) CharPolys_5x5.tar.gz (7MB)

Minimal Polynomials

Download all minimal polynomials:

Matrix Size .csv .zip .tar.gz
1x1 MinPolys_1x1.csv (36B) MinPolys_1x1.zip (207B) MinPolys_1x1.tar.gz (157B)
2x2 MinPolys_2x2.csv (203B) MinPolys_2x2.zip (275B) MinPolys_2x2.tar.gz (226B)
3x3 MinPolys_3x3.csv (3KB) MinPolys_3x3.zip (1008B) MinPolys_3x3.tar.gz (986B)
4x4 MinPolys_4x4.csv (150KB) MinPolys_4x4.zip (41KB) MinPolys_4x4.tar.gz (41KB)

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