Kronecker Product

Kronecker product, sometimes denoted by $\otimes$ , is an operation on two matrices of arbitrary size resulting in a block matrix.

The Kronecker product is also sometimes called matrix direct product.

If $A$ is an $m \times n$ matrix and $B$ is a $p \times q$ matrix, then the Kronecker product $A \otimes B$ is the $p m \times q n$ block matrix.

A \otimes B = a_{11} B ⋮ a_{m 1} B \dots ⋱ \dots a_{1 n} B ⋮ a_{mn} B

more explicitly:

각 원소는 $(A \otimes B)_{i, j} = a_{⌈ i / p ⌉, ⌈ j / q]} b_{(i - 1) % p + 1, (j - 1) % q + 1}$ 으로 표시될 수 있다 ( $i, j$ 가 $1$ 부터 시작).

B) Example

[1324] \otimes [0657] = 1 [0657] 3 [0657] 2 [0657] 4 [0657] = 1 \times 0 1 \times 6 3 \times 0 3 \times 6 1 \times 5 1 \times 7 3 \times 5 3 \times 7 2 \times 0 2 \times 6 4 \times 0 4 \times 6 2 \times 5 2 \times 7 4 \times 5 4 \times 7 = 0601857152101202410142028