Bohemian Matrices

Unstructured_0_Diag_n1_1

Matrices with entries from the set {-1, +1} and diagonal entries fixed at 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
2x2 CharPolys_2x2.csv (35B) CharPolys_2x2.zip (212B) CharPolys_2x2.tar.gz (162B)
3x3 CharPolys_3x3.csv (90B) CharPolys_3x3.zip (238B) CharPolys_3x3.tar.gz (183B)
4x4 CharPolys_4x4.csv (417B) CharPolys_4x4.zip (332B) CharPolys_4x4.tar.gz (288B)
5x5 CharPolys_5x5.csv (4KB) CharPolys_5x5.zip (1KB) CharPolys_5x5.tar.gz (1KB)
6x6 CharPolys_6x6.csv (124KB) CharPolys_6x6.zip (25KB) CharPolys_6x6.tar.gz (25KB)

Minimal Polynomials

Download all minimal polynomials:

Matrix Size .csv .zip .tar.gz
2x2 MinPolys_2x2.csv (37B) MinPolys_2x2.zip (211B) MinPolys_2x2.tar.gz (161B)
3x3 MinPolys_3x3.csv (96B) MinPolys_3x3.zip (241B) MinPolys_3x3.tar.gz (186B)
4x4 MinPolys_4x4.csv (520B) MinPolys_4x4.zip (372B) MinPolys_4x4.tar.gz (327B)
5x5 MinPolys_5x5.csv (5KB) MinPolys_5x5.zip (2KB) MinPolys_5x5.tar.gz (2KB)

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 A053763        
2x2 4 2 2 4 1
3x3 64 6 6 56 3
4x4 4,096 27 32 3,328 9
5x5 1,048,576 222 260 830,912 25
6x6 1,073,741,824 5,091     125

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        
2x2 4 2 2 2
3x3 11 5 6 6
4x4 60 20 40 32
5x5 635 169 466 260
6x6 21,686 5,652 16,034  

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                
2x2 0 4 0 4        
3x3 32 32 0 32 32      
4x4 0 4,096 0 0 0 4,096    
5x5 203,776 844,800 0 0 0 203,776 844,800  
6x6 0 1,073,741,824            

Determinant

Matrix Size Number of Distinct Determinants Maximum Determinant Number of Unimodular Matrices
OEIS      
2x2 2 1 4
3x3 3 2 0
4x4 8 9 1,920
5x5 19 22 0
6x6 74 125 146,227,200

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            
2x2     0      
3x3     0      
4x4     0      
5x5     0      
6x6     0