Bohemian Matrices

Unstructured_n1_1

Matrices with entries from the set {-1, +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 (27B) CharPolys_1x1.zip (208B) CharPolys_1x1.tar.gz (157B)
2x2 CharPolys_2x2.csv (69B) CharPolys_2x2.zip (230B) CharPolys_2x2.tar.gz (176B)
3x3 CharPolys_3x3.csv (353B) CharPolys_3x3.zip (307B) CharPolys_3x3.tar.gz (260B)
4x4 CharPolys_4x4.csv (3KB) CharPolys_4x4.zip (908B) CharPolys_4x4.tar.gz (883B)
5x5 CharPolys_5x5.csv (64KB) CharPolys_5x5.zip (12KB) CharPolys_5x5.tar.gz (12KB)
6x6 CharPolys_6x6.csv (3MB) CharPolys_6x6.zip (524KB) CharPolys_6x6.tar.gz (524KB)

Minimal Polynomials

Download all minimal polynomials:

Matrix Size .csv .zip .tar.gz
1x1 MinPolys_1x1.csv (29B) MinPolys_1x1.zip (207B) MinPolys_1x1.tar.gz (156B)
2x2 MinPolys_2x2.csv (75B) MinPolys_2x2.zip (229B) MinPolys_2x2.tar.gz (176B)
3x3 MinPolys_3x3.csv (407B) MinPolys_3x3.zip (320B) MinPolys_3x3.tar.gz (273B)
4x4 MinPolys_4x4.csv (4KB) MinPolys_4x4.zip (1KB) MinPolys_4x4.tar.gz (1KB)
5x5 MinPolys_5x5.csv (71KB) MinPolys_5x5.zip (16KB) MinPolys_5x5.tar.gz (16KB)

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 A272662 A306782 A306816  
1x1 2 2 2 2 1
2x2 16 6 6 16 2
3x3 512 28 30 472 6
4x4 65,536 203 223 57,456 16
5x5 33,554,432 3,150 3,408 29,025,984 80
6x6 68,719,476,736 131,641     288

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 A306791 A306794    
1x1 2 2 0 2
2x2 9 5 4 6
3x3 35 15 20 30
4x4 335 119 236 232
5x5 7,709 2,297 5,412 3,490
6x6 510,743 145,213 365,530  

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 A057982 A056990            
1x1 0 2 2          
2x2 8 8 8 8        
3x3 320 192 32 288 192      
4x4 43,264 22,272 128 6,272 36,864 22,272    
5x5 22,003,712 11,550,720 512 115,200 3,456,000 18,432,000 11,550,720  
6x6 43,090,149,376 25,629,327,360            

Determinant

Matrix Size Number of Distinct Determinants Maximum Determinant Number of Unimodular Matrices
OEIS   A003433  
1x1 2 1 2
2x2 3 2 0
3x3 3 4 0
4x4 5 16 0
5x5 7 48 0
6x6 11 160 0

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     A306819      
1x1     0      
2x2     4      
3x3     0      
4x4     2,064      
5x5     0      
6x6     100,172,800