Matrix-Matrix Product

linear-algebra

Definition

Matrix-Matrix Product

Let $A\in F^{m\times n}$ and $B\in F^{n\times p}$ be matrices over a field $F$. The matrix-matrix product is the operation

$$\cdot :F^{m\times n}\times F^{n\times p}\to F^{m\times p}$$

defined by

$$(AB{)}_{ik}=\sum _{j=1}^n{A}_{ij}{B}_{jk}$$

for all $1\le i\le m$, $1\le k\le p$.

Einstein Notation: $(AB{)}_{ik}=A_{ij}{B}_{jk}$.