JGD_CAG/CAG_mat72
CAG matrix set from Michael Monagan, Simon Fraser Univ., Canada
Name 
CAG_mat72 
Group 
JGD_CAG 
Matrix ID 
1943 
Num Rows

72 
Num Cols

72 
Nonzeros

1,012 
Pattern Entries

1,012 
Kind

Combinatorial Problem 
Symmetric

No 
Date

2008 
Author

M. Monagan 
Editor

J.G. Dumas 
Structural Rank 
72 
Structural Rank Full 
true 
Num Dmperm Blocks

6 
Strongly Connect Components

6 
Num Explicit Zeros

0 
Pattern Symmetry

55.7% 
Numeric Symmetry

33.4% 
Cholesky Candidate

no 
Positive Definite

no 
Type

integer 
SVD Statistics 
Matrix Norm 
6.090033e+01 
Minimum Singular Value 
6.931388e03 
Condition Number 
8.786167e+03

Rank 
72 
sprank(A)rank(A) 
0 
Null Space Dimension 
0 
Full Numerical Rank? 
yes 
Download Singular Values 
MATLAB

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Notes 
CAG matrix set from Michael Monagan, Simon Fraser Univ., Canada
From JeanGuillaume Dumas' Sparse Integer Matrix Collection,
http://ljk.imag.fr/membres/JeanGuillaume.Dumas/simc.html
Strongly Connected Graph Components and Computing
Characteristic Polynomials of Integer Matrices in Maple,
Simon Lo, Michael Monagan, Allan Wittkopf
{sclo,mmonagan,wittkopf} at cecm.sfu.ca
Centre for Experimental and Constructive Mathematics,
Department of Mathematics, Simon Fraser University,
Burnaby, B.C., V5A 1S6, Canada.
abstract:
Let A be an n x n matrix of integers. We present details of our Maple
implementation of a simple modular method for computing the
characteristic polynomial of A. We consider several different
representations for the computation modulo primes, in particular, the
use of double precision floats. The algorithm used in Maple releases
710 is the Berkowitz algorithm. We present some timings comparing the
two algorithms on a sequence of matrices arising from an application in
combinatorics of Jocelyn Quaintance. These matrices have a hidden block
structure. Once identified, we can further reduce the computing time
dramatically. This work has been incorporated into Maple 11's
LinearAlgebra package.
http://www.cecm.sfu.ca/~monaganm/papers/CP8.pdf
Filename in JGD collection: CAG/mat72.sms
