Matrix properties
number of rows	544
number of columns	637
nonzeros	6,153
structural full rank?	no
structural rank	542
# of blocks from dmperm	2
# strongly connected comp.	8
explicit zero entries	0
nonzero pattern symmetry	0%
numeric value symmetry	0%
type	integer
structure	rectangular
Cholesky candidate?	no
positive definite?	no

author	P. Elbaz-Vincent
editor	J.-G. Dumas
date	2008
kind	combinatorial problem
2D/3D problem?	no

Notes:

Differentials of the Voronoi complex of perfect forms of rank 6 mod GL_6(Z),
from Philippe Elbaz-Vincent, Institut Fourier, Grenoble, France.            
                                                                            
From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,                
http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html                   
                                                                            
http://www-fourier.ujf-grenoble.fr/-Informations-personnelles-.html?P=pev   
                                                                            
D_6  Smith Invariants = [ 1:156 ]                                           
D_7  Smith Invariants = [ 1:307 2:3 60:2 ]                                  
D_8  Smith Invariants = [ 1:320 2:1 6:2 12:1 ]                              
D_9  Smith Invariants = [ 1:217 2:3 ]                                       
D_10 Smith Invariants = [ 1:120 ]                                           
                                                                            
Filename in JGD collection: GL6/D_8.sms                                     

Ordering statistics:	result
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	125,445
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	110,076

SVD-based statistics:
norm(A)	15.2984
min(svd(A))	5.52056e-31
cond(A)	2.77117e+31
rank(A)	324
sprank(A)-rank(A)	218
null space dimension	220
full numerical rank?	no
singular value gap	3.48224e+14

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.