CAG matrix set from Michael Monagan, Simon Fraser Univ., Canada
Name CAG_mat72
Matrix ID 1943
Num Rows 72
Num Cols 72
Nonzeros 1,012
Pattern Entries 1,012
Kind Combinatorial Problem
Symmetric No
Date 2008
Author M. Monagan
Editor J.-G. Dumas
Structural Rank 72
Structural Rank Full true
Num Dmperm Blocks 6
Strongly Connect Components 6
Num Explicit Zeros 0
Pattern Symmetry 55.7%
Numeric Symmetry 33.4%
Cholesky Candidate no
Positive Definite no
Type integer
SVD Statistics
Matrix Norm 6.090033e+01
Minimum Singular Value 6.931388e-03
Condition Number 8.786167e+03
Rank 72
sprank(A)-rank(A) 0
Null Space Dimension 0
Full Numerical Rank? yes
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CAG matrix set from Michael Monagan, Simon Fraser Univ., Canada        
From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,           
Strongly Connected Graph Components and Computing                      
Characteristic Polynomials of Integer Matrices in Maple,               
Simon Lo, Michael Monagan, Allan Wittkopf                              
{sclo,mmonagan,wittkopf} at cecm.sfu.ca                                
Centre for Experimental and Constructive Mathematics,                  
Department of Mathematics, Simon Fraser University,                    
Burnaby, B.C., V5A 1S6, Canada.                                        
Let A be an n x n matrix of integers. We present details of our Maple  
implementation of a simple modular method for computing the            
characteristic polynomial of A.  We consider several different         
representations for the computation modulo primes, in particular, the  
use of double precision floats.  The algorithm used in Maple releases  
7-10 is the Berkowitz algorithm. We present some timings comparing the 
two algorithms on a sequence of matrices arising from an application in
combinatorics of Jocelyn Quaintance. These matrices have a hidden block
structure. Once identified, we can further reduce the computing time   
dramatically.  This work has been incorporated into Maple 11's         
LinearAlgebra package.                                                 
Filename in JGD collection: CAG/mat72.sms