Kronecker product ↩

Metadata

shorthands: {}
aliases: [Matrix direct product, Zehfuss product, Zehfuss matrix]
created: 2021-12-04 18:00:39
modified: 2022-01-10 04:13:04

The Kronecker product is an operation on two matrices of arbitrary size, resulting in a block matrix.

It gives back the matrix of the tensor product of the represented linear maps.

Definition

If is an matrix and is a matrix, then the Kronecker product is the block matrix:

And more explicitly:

It is a generalization of the outer product
If and represent linear transformations and , then represents the tensor product of the two maps,
For , matrices and , vectors, (vector is Outer product)