K = kron(X,Y)
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
.
X
is 2-by-3, then kron(X,Y)
is
The matrix representation of the discrete Laplacian operator on a two-dimensional,[ X(1,1)
*Y X(1,2)
*Y X(1,3)
*Y
X(2,1)
*Y X(2,2)
*Y X(2,3)
*Y ]
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.