Matrix Multiplication

linear-algebra

Definition

Matrix Multiplication

Let $A=(a_{ij})\in F^{m\times n}$ and $B=(b_{jk})\in F^{n\times q}$ be two matrices. Then their product $A\cdot B$ is the $m\times q$ matrix $C=(c_{ik})$ with entries

$$c_{ik}=\sum _{j=1}^n{a}_{ij}{b}_{jk}=⟨A_{i,\ast },B_{\ast ,k}⟩$$

The entry in row $i$ and column $k$ is obtained by taking the dot product of the $i$-th row of $A$ with the $k$-th column of $B$.