Re: How to write a matrix in a block form?
- From: israel@xxxxxxxxxxx (Robert Israel)
- Date: 2 Dec 2005 20:40:29 GMT
In article <dmpnuo$2tot$1@xxxxxxxxxxxxxxx>,
Pavel Pokorny <Pavel.Pokorny@xxxxxxxxxxxxxxxxxxxxxxx> wrote:
>is there an algorithm to express a given sparse matrix
>(with integer entries)
>in a block form?
>
>I want to find "invariant" subspaces of the problem A.x=b
I'm not sure exactly what you mean, but perhaps it is this:
if the matrix A is n x n, partition the set {1,...,n} into
as many sets as possible with the property that A_{i,j} = 0
if i and j are in different sets of the partition.
You can solve this by looking at the graph with vertices
1,...,n, and an edge (i,j) if A_{i,j} <> 0. Then what you
want are the connected components of the graph. It's
easy to find them, e.g. by depth-first search.
Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.
- References:
- How to write a matrix in a block form?
- From: Pavel Pokorny
- How to write a matrix in a block form?
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