Matrix multiplication/Definition

Let ${\displaystyle {}K}$ denote a field, and let ${\displaystyle {}A}$ denote an ${\displaystyle {}m\times n}$-matrix and ${\displaystyle {}B}$ an ${\displaystyle {}n\times p}$-matrix over ${\displaystyle {}K}$. Then the matrix product

${\displaystyle AB}$

is the ${\displaystyle {}m\times p}$-matrix, whose entries are given by

${\displaystyle {}c_{ik}=\sum _{j=1}^{n}a_{ij}b_{jk}\,.}$