Matrix properties
number of rows	30
number of columns	77
nonzeros	251
structural full rank?	yes
structural rank	30
# of blocks from dmperm	1
# strongly connected comp.	35
explicit zero entries	0
nonzero pattern symmetry	0%
numeric value symmetry	0%
type	integer
structure	rectangular
Cholesky candidate?	no
positive definite?	no

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

Notes:

Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery.
Univ. Paris Sud.                                                               
                                                                               
From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,                   
http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html                      
                                                                               
http://www.lapcs.univ-lyon1.fr/~nthiery/LinearAlgebra/                         
                                                                               
Linear Algebra for combinatorics                                               
                                                                               
Abstract:  Computations in algebraic combinatorics often boils down to         
sparse linear algebra over some exact field. Such computations are             
usually done in high level computer algebra systems like MuPAD or              
Maple, which are reasonnably efficient when the ground field requires          
symbolic computations. However, when the ground field is, say Q  or            
Z/pZ, the use of external specialized libraries becomes necessary. This        
document, geared toward developpers of such libraries, present a brief         
overview of my needs, which seems to be fairly typical in the                  
community.                                                                     
                                                                               
IG5-6: 30 x 77 : rang = 30  (Iteratif: 0.01 s, Gauss: 0.01 s)                  
IG5-7: 62 x 150 : rang = 62  (Iteratif: 0.02 s, Gauss: 0.01 s)                 
IG5-8: 156 x 292 : rang = 154  (Iteratif: 0.08 s, Gauss: 0.01 s)               
IG5-9: 342 x 540 : rang = 308  (Iteratif: 0.46 s, Gauss: 0.02 s)               
IG5-10: 652 x 976 : rang = 527  (Iteratif: 2.1 s, Gauss: 0.07 s)               
IG5-11: 1227 x 1692 : rang = 902  (Iteratif: 7.5 s, Gauss: 0.22 s)             
IG5-12: 2296 x 2875 : rang = 1578  (Iteratif: 26 s, Gauss: 0.93 s)             
IG5-13: 3994 x 4731 : rang = 2532  (Iteratif: 80 s, Gauss: 3.35 s)             
IG5-14: 6727 x 7621 : rang = 3906  (Iteratif: 244 s, Gauss: 10.06 s)           
IG5-15: 11358 x 11987 : rang = 6146  (Iteratif: s, Gauss: 29.74 s)             
IG5-16: 18485 x 18829 : rang = 9519  (Iteratif: s, Gauss: 621.97 s)            
IG5-17: 27944 x 30131 : rang = 14060  (Iteratif: s, Gauss: 1973.8 s)           
                                                                               
Filename in JGD collection: G5/IG5-6.txt2                                      

Ordering statistics:	result
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	461
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	400

SVD-based statistics:
norm(A)	28.3867
min(svd(A))	0.181445
cond(A)	156.449
rank(A)	30
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 (R)) ; where [~,R,E] = spqr (A') with droptol of zero
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.