Matrix properties
number of rows	3,159
number of columns	15,905
nonzeros	2,872,265
structural full rank?	yes
structural rank	3,159
# of blocks from dmperm	1
# strongly connected comp.	2
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:

Brute force disjoint product matrices in tree algebra on n nodes, Nicolas Thiery
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.                                                                      
                                                                                
Filename in JGD collection: Kocay/Trec14.txt2                                   

Ordering statistics:	result
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	35,970,189
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	4,741,823

SVD-based statistics:
norm(A)	6088.53
min(svd(A))	6.03279e-14
cond(A)	1.00924e+17
rank(A)	3,133
sprank(A)-rank(A)	26
null space dimension	26
full numerical rank?	no
singular value gap	2.8318e+12

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.