# kron

## Purpose

Kronecker tensor product.

## Synopsis

    K = kron(X,Y)

## Description

`kron(X`,`Y)` is the Kronecker tensor product of `X` and `Y`. The result is a large matrix formed by taking all possible products between the elements of `X` and those of `Y`. If `X` is `m`-by-`n` and `Y` is `p`-by-`q`, then `kron(X,Y)` is `m*p`-by-`n*q`.

## Examples

If `X` is 2-by-3, then `kron(X,Y)` is

    [ X(1,1)*Y X(1,2)*Y X(1,3)*Y
      X(2,1)*Y X(2,2)*Y X(2,3)*Y ]

The matrix representation of the discrete Laplacian operator on a two-dimensional, `n`-by-`n` grid is a `n^2`-by-`n^2` sparse matrix. There are at most five nonzero elements in each row or column. The matrix can be generated as the Kronecker product of one-dimensional difference operators with the following statements.

     I = speye(n,n);
     E = sparse(2:n,1:n-1,1,n,n);
     D = E+E'-2*I;
     A = kron(D,I)+kron(I,D);

(c) Copyright 1994 by The MathWorks, Inc.