ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Countable map
Array
Matrix
Real collection matrix
Complex matrix
Definition D5191
Complex matrix kronecker product
Formulation 0
Let $A \in \mathbb{C}^{N \times M}$ and $B \in \mathbb{C}^{K \times H}$ each be a D999: Complex matrix.
The kronecker product of $(A, B)$ is the D999: Complex matrix \begin{equation} \begin{bmatrix} A_{1, 1} B & A_{1, 2} B & \cdots & A_{1, M} B \\ A_{2, 1} B & A_{2, 2} B & \vdots & A_{2, M} B \\ \vdots & \cdots & \ddots & \vdots \\ A_{N, 1} B & A_{N, 2} B & \cdots & A_{N, M} B \end{bmatrix} \in \mathbb{C}^{N K \times M H} \end{equation}