Matrix properties
number of rows	72
number of columns	72
nonzeros	1,012
structural full rank?	yes
structural rank	72
# of blocks from dmperm	6
# strongly connected comp.	6
explicit zero entries	0
nonzero pattern symmetry	56%
numeric value symmetry	33%
type	integer
structure	unsymmetric
Cholesky candidate?	no
positive definite?	no

author	M. Monagan
editor	J.-G. Dumas
date	2008
kind	combinatorial problem
2D/3D problem?	no

Notes:

CAG matrix set from Michael Monagan, Simon Fraser Univ., Canada        
From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,           
http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html              
                                                                       
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.                                        
                                                                       
abstract:                                                              
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.                                                 
                                                                       
http://www.cecm.sfu.ca/~monaganm/papers/CP8.pdf                        
                                                                       
Filename in JGD collection: CAG/mat72.sms                              

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	875
Cholesky flop count	1.3e+04
nnz(L+U), no partial pivoting, with AMD	1,678
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	865
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	1,107

SVD-based statistics:
norm(A)	60.9003
min(svd(A))	0.00693139
cond(A)	8786.17
rank(A)	72
sprank(A)-rank(A)	0
null space dimension	0
full numerical rank?	yes

singular values (MAT file):	click here
SVD method used:	s = svd (full (A)) ;
status:	ok

For a description of the statistics displayed above, click here.

Maintained by Tim Davis, last updated 12-Mar-2014.
Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.