JGD_G5/IG5-7

Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery.
Name IG5-7
Group JGD_G5
Matrix ID 1966
Num Rows 62
Num Cols 150
Nonzeros 549
Pattern Entries 549
Kind Combinatorial Problem
Symmetric No
Date 2008
Author N. Thiery
Editor J.-G. Dumas
Structural Rank 62
Structural Rank Full true
Num Dmperm Blocks 1
Strongly Connect Components 76
Num Explicit Zeros 0
Pattern Symmetry 0%
Numeric Symmetry 0%
Cholesky Candidate no
Positive Definite no
Type integer
SVD Statistics
Matrix Norm 3.014322e+01
Minimum Singular Value 1.155959e-01
Condition Number 2.607637e+02
Rank 62
sprank(A)-rank(A) 0
Null Space Dimension 0
Full Numerical Rank? yes
Download Singular Values MATLAB
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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/IG5-7.txt2