Bohemian Matrices

Unstructured_0_Diag_0_1_2

Matrices with entries from the set {0, +1, +2} 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 (53B) CharPolys_2x2.zip (222B) CharPolys_2x2.tar.gz (168B)
3x3 CharPolys_3x3.csv (543B) CharPolys_3x3.zip (357B) CharPolys_3x3.tar.gz (313B)
4x4 CharPolys_4x4.csv (39KB) CharPolys_4x4.zip (8KB) CharPolys_4x4.tar.gz (8KB)
5x5 CharPolys_5x5.csv (19MB) CharPolys_5x5.zip (3MB) CharPolys_5x5.tar.gz (3MB)

Minimal Polynomials

Download all minimal polynomials:

Matrix Size .csv .zip .tar.gz
2x2 MinPolys_2x2.csv (66B) MinPolys_2x2.zip (225B) MinPolys_2x2.tar.gz (173B)
3x3 MinPolys_3x3.csv (618B) MinPolys_3x3.zip (382B) MinPolys_3x3.tar.gz (341B)
4x4 MinPolys_4x4.csv (42KB) MinPolys_4x4.zip (10KB) MinPolys_4x4.tar.gz (10KB)

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 4 5 8 4
3x3 729 42 45 690 16
4x4 531,441 2,329 2,372 515,970 64
5x5 3,486,784,401 871,436     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        
2x2 7 7 0 5
3x3 98 62 36 45
4x4 8,141 4,629 3,512 2,373
5x5 4,190,019 2,064,975 2,125,044  

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 361 368 36 324 368    
4x4 198,736 332,705 220 12,904 185,611 332,705  
5x5 907,245,701 2,579,538,700          

Determinant

Matrix Size Number of Distinct Determinants Maximum Determinant Number of Unimodular Matrices
OEIS      
2x2 4 4 1
3x3 12 16 38
4x4 48 48 18,537
5x5 200 160 74,446,524

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