conformal partitioning

Let R be a ring. Let the matrices AMm,n(R) and BMn,p(R) be partitioned into submatricesMathworldPlanetmath Ai,j and Bi,j respectively as follows:


where Ai,j is mi×nj,i=1gmi=m, j=1hnj=n;


where Bi,j is ni×pj, j=1kpj=p. Then A and B (in this ) are said to be conformally partitioned for multiplication.

Now suppose that A and B are conformally partitioned for multiplication. Let C=AB be partitioned as follows:


where Ci,j is mi×pj, i=1,,g, j=1,,k. Then


This method of computing AB is sometimes called block multiplication.

Title conformal partitioning
Canonical name ConformalPartitioning
Date of creation 2013-03-22 16:04:16
Last modified on 2013-03-22 16:04:16
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 9
Author Mathprof (13753)
Entry type Definition
Classification msc 15-00
Defines block multiplication