Kronecker Product with SparseArray

*To*: mathgroup at smc.vnet.net*Subject*: [mg62108] Kronecker Product with SparseArray*From*: Cyrus F Hirjibehedin <hirjibe at us.ibm.com>*Date*: Fri, 11 Nov 2005 02:52:39 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

To Mathgroup: I'm trying to implement a function in Mathematica 5.2 to take the Kronecker Product of two large sparse matrices. The simplest suggested way to do this seems to be BlockMatrix[Outer[Times, X, Y]] where X and Y are two matrices. The BlockMatrix is necessary because Outer produces a matrix of matrices, rather than a matrix of elements, and this is not compatible with functions like Eigenvalues or Eigensystem. What I would like to do is pass in X and Y as SparseArray types and have the result produce a SparseArray type that I can pass to functions like Eigenvalues or Eigensystem. Right now, I'm doing this with SparseArray[BlockMatrix[Outer[Times, X, Y]]] where X and Y are SparseArray types. The problem is that I run out of memory when trying to compute large matrices. I think the problem is that when BlockMatrix tries to "flatten" the results of Outer it first generates the full dense matrix representation, which is too big either for it or for SparseArray to handle. Does anyone know how to turn the results of Outer[Times,X,Y]] into an object that is a SparseArray type that can be passed to things like Eigenvalues or Eigensystem? or Does anyone know of a different way to directly compute the Kronecker Product of two matrices represented as SparseArray types and have the output be a SparseArray type that can be passed to Eigenvalues without generating an intermediate dense matrix representation? Any advice would be greatly appreciated. Sincerely, Cyrus -- Cyrus F. Hirjibehedin hirjibe at us.ibm.com

**Follow-Ups**:**Re: Kronecker Product with SparseArray***From:*"Carl K. Woll" <carl@woll2woll.com>