Bohemian Matrices

Unstructured_0_Diag_n1_0_1

Matrices with entries from the set {-1, 0, +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 (43B) CharPolys_2x2.zip (216B) CharPolys_2x2.tar.gz (164B)
3x3 CharPolys_3x3.csv (257B) CharPolys_3x3.zip (285B) CharPolys_3x3.tar.gz (234B)
4x4 CharPolys_4x4.csv (6KB) CharPolys_4x4.zip (1KB) CharPolys_4x4.tar.gz (1KB)
5x5 CharPolys_5x5.csv (731KB) CharPolys_5x5.zip (137KB) CharPolys_5x5.tar.gz (137KB)

Minimal Polynomials

Download all minimal polynomials:

Matrix Size .csv .zip .tar.gz
2x2 MinPolys_2x2.csv (55B) MinPolys_2x2.zip (222B) MinPolys_2x2.tar.gz (169B)
3x3 MinPolys_3x3.csv (299B) MinPolys_3x3.zip (296B) MinPolys_3x3.tar.gz (248B)
4x4 MinPolys_4x4.csv (6KB) MinPolys_4x4.zip (2KB) MinPolys_4x4.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 A053764        
2x2 9 3 4 8 1
3x3 729 20 22 684 3
4x4 531,441 381 404 506,472 9
5x5 3,486,784,401 38,145     25

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 5 3 2 4
3x3 43 17 26 22
4x4 1,161 363 798 405
5x5 170,935 52,981 117,954  

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              
2x2 5 4 4 4      
3x3 393 336 36 356 356    
4x4 236,833 294,608 232 16,728 219,872 294,608  
5x5 1,234,304,529 2,252,479,872          

Determinant

Matrix Size Number of Distinct Determinants Maximum Determinant Number of Unimodular Matrices
OEIS      
2x2 3 1 4
3x3 5 2 304
4x4 15 9 182,544
5x5 43 22 848,818,816

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     5      
3x3     133      
4x4     18,905      
5x5     13,998,201