Brute force disjoint product matrices in tree algebra on n nodes, Nicolas Thiery
Name Trec14
Group JGD_Kocay
Matrix ID 2148
Num Rows 3,159
Num Cols 15,905
Nonzeros 2,872,265
Pattern Entries 2,872,265
Kind Combinatorial Problem
Symmetric No
Date 2008
Author N. Thiery
Editor J.-G. Dumas
Structural Rank 3,159
Structural Rank Full true
Num Dmperm Blocks 1
Strongly Connect Components 2
Num Explicit Zeros 0
Pattern Symmetry 0%
Numeric Symmetry 0%
Cholesky Candidate no
Positive Definite no
Type integer
SVD Statistics
Matrix Norm 6.088528e+03
Minimum Singular Value 6.032788e-14
Condition Number 1.009240e+17
Rank 3,133
sprank(A)-rank(A) 26
Null Space Dimension 26
Full Numerical Rank? no
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Brute force disjoint product matrices in tree algebra on n nodes, Nicolas Thiery
From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,                    
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                   
Filename in JGD collection: Kocay/Trec14.txt2