Bohemian Matrices

Unstructured_0_1_2

Matrices with entries from the set {0, +1, +2}.

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 (34B) CharPolys_1x1.zip (210B) CharPolys_1x1.tar.gz (159B)
2x2 CharPolys_2x2.csv (226B) CharPolys_2x2.zip (280B) CharPolys_2x2.tar.gz (231B)
3x3 CharPolys_3x3.csv (7KB) CharPolys_3x3.zip (2KB) CharPolys_3x3.tar.gz (2KB)
4x4 CharPolys_4x4.csv (985KB) CharPolys_4x4.zip (206KB) CharPolys_4x4.tar.gz (206KB)
5x5 CharPolys_5x5.csv (866MB) CharPolys_5x5.zip (146MB) CharPolys_5x5.tar.gz (146MB)

Minimal Polynomials

Download all minimal polynomials:

Matrix Size .csv .zip .tar.gz
1x1 MinPolys_1x1.csv (37B) MinPolys_1x1.zip (209B) MinPolys_1x1.tar.gz (158B)
2x2 MinPolys_2x2.csv (277B) MinPolys_2x2.zip (289B) MinPolys_2x2.tar.gz (243B)
3x3 MinPolys_3x3.csv (7KB) MinPolys_3x3.zip (2KB) MinPolys_3x3.tar.gz (2KB)
4x4 MinPolys_4x4.csv (1MB) MinPolys_4x4.zip (286KB) MinPolys_4x4.tar.gz (286KB)

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 A272659 A306783 A306818  
1x1 3 3 3 3 2
2x2 81 22 25 78 4
3x3 19,683 513 532 19,068 16
4x4 43,046,721 58,335 58,693 42,300,060 64
5x5 847,288,609,443 40,422,490     240

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 A306792 A306795    
1x1 3 3 0 3
2x2 25 25 0 25
3x3 1,027 657 370 536
4x4 193,244 112,870 80,374 58,762
5x5        

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 A306840 A197487          
1x1 1 2 2        
2x2 31 50 50 30      
3x3 6,891 12,792 266 6,624 12,792    
4x4 12,202,161 30,844,560 1,950 388,946 11,811,264 30,844,560  
5x5 175,419,087,483 671,869,521,960          

Determinant

Matrix Size Number of Distinct Determinants Maximum Determinant Number of Unimodular Matrices
OEIS      
1x1 3 2 1
2x2 9 4 14
3x3 25 16 2,022
4x4 67 48 2,699,544
5x5 233 160 31,519,662,120

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     5      
3x3     109      
4x4     9,449      
5x5     3,068,281