Kronecker Product

Author

Eric W. Weisstein
February 7, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/LinearAlgebra/KroneckerProduct.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/KroneckerProduct.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Examples

KroneckerProduct[{{1,2},{3,4}},{{0,5},{6,7}}]//TraditionalForm

a={{1,2},{0,1}};
b={{1,1,1},{2,2,2},{3,3,3},{4,4,4}};
{a//MatrixForm, b//MatrixForm,KroneckerProduct[a,b]//MatrixForm}

aa={{(Subscript[a, 11]),(Subscript[a, 12])},{(Subscript[a, 21]),(Subscript[a, 22])}};
bb={{(Subscript[b, 11]),(Subscript[b, 12])},{(Subscript[b, 21]),(Subscript[b, 22])},{(Subscript[b, 31]),(Subscript[b, 32])}};

{aa//MatrixForm,bb//MatrixForm,KroneckerProduct[aa,bb]//MatrixForm}

Outer[Times,aa,bb]//MatrixForm

<<LinearAlgebra`MatrixManipulation`

BlockMatrix[Outer[Times,aa,bb]]//MatrixForm