`kron`

Kronecker tensor product of two matrices.

Category: Mathematics > Linear Algebra

Syntax

K = kron(A, B)

Replaces each entry A(i,j) by the block A(i,j)*B.

Description

The Kronecker product arranges all the products of one entry of A with one entry of B into a large block matrix. It is not commutative. It is used to build operators on tensor-product spaces, for example the 2-D Laplacian from 1-D ones, and satisfies (A kron B)(C kron D) = (A*C) kron (B*D).

Input arguments

A, B: Numeric arrays of any size.

Output arguments

K: Matrix of size [size(A,1)*size(B,1), size(A,2)*size(B,2)].

Example

Block structure

kron([1 2], [1; 1])
kron(eye(2), [1 2; 3 4])

Output

ans = 2×2

     1     2
     1     2
ans = 4×4

     1     2     0     0
     3     4     0     0
     0     0     1     2
     0     0     3     4

See also

mtimes repmat eye cross