---- > [!definition] Definition. ([[Kronecker product]]) > The **Kronecker product** of two [[matrix|matrices]] $\b A \in \mathbb{F}^{m \times n}, \b B \in \mathbb{F}^{k \times \ell}$ is defined to be $\b A \otimes \b B = \begin{bmatrix} a_{11}\b B & a_{12} \b B & \dots & a_{1n}\b B \\ & & \ddots & \\ a_{m1} \b B & a_{m 2} \b B & \dots & a_{mn}\b B \end{bmatrix} \in \mathbb{F}^{(mk) \times (n \ell)},$ i.e., $[\b A \otimes \b B]_{ij}=A_{\lceil \frac{i}{k} \rceil, \lceil \frac{j}{\ell} \rceil }B_{i \text{ mod }k, j \text{ mod } \ell}.$ ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```