Bohemian Matrices

Unstructured_0_Diag_n1_0

Matrices with entries from the set {-1, 0} 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 (214B) CharPolys_2x2.tar.gz (163B)
3x3 CharPolys_3x3.csv (99B) CharPolys_3x3.zip (245B) CharPolys_3x3.tar.gz (188B)
4x4 CharPolys_4x4.csv (688B) CharPolys_4x4.zip (398B) CharPolys_4x4.tar.gz (358B)
5x5 CharPolys_5x5.csv (13KB) CharPolys_5x5.zip (3KB) CharPolys_5x5.tar.gz (3KB)
6x6 CharPolys_6x6.csv (771KB) CharPolys_6x6.zip (133KB) CharPolys_6x6.tar.gz (133KB)

Minimal Polynomials

Download all minimal polynomials:

Matrix Size .csv .zip .tar.gz
2x2 MinPolys_2x2.csv (46B) MinPolys_2x2.zip (218B) MinPolys_2x2.tar.gz (166B)
3x3 MinPolys_3x3.csv (129B) MinPolys_3x3.zip (254B) MinPolys_3x3.tar.gz (199B)
4x4 MinPolys_4x4.csv (878B) MinPolys_4x4.zip (455B) MinPolys_4x4.tar.gz (416B)
5x5 MinPolys_5x5.csv (15KB) MinPolys_5x5.zip (4KB) MinPolys_5x5.tar.gz (4KB)

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 3 3 1
3x3 64 7 9 50 3
4x4 4,096 46 56 3,218 8
5x5 1,048,576 718 791 851,592 20
6x6 1,073,741,824 35,237     45

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 3 3 0 3
3x3 13 9 4 9
4x4 118 68 50 57
5x5 2,604 1,230 1,374 794
6x6 178,810 75,840 102,970  

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 3 1 2 1        
3x3 49 15 12 36 15      
4x4 2,992 1,104 50 673 2,268 1,104    
5x5 717,106 331,470 180 9,060 140,325 567,540 331,470  
6x6 671,231,704 402,510,120            

Determinant

Matrix Size Number of Distinct Determinants Maximum Determinant Number of Unimodular Matrices
OEIS      
2x2 2 1 1
3x3 3 2 14
4x4 5 3 975
5x5 10 5 259,944
6x6 19 9 264,707,175

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     3      
3x3     25      
4x4     543      
5x5     29,281      
6x6     3,781,503