Matrix multiplication/Definition

Matrix multiplication

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

$AB$

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

$c_{ik}=\sum _{j=1}^n{a}_{ij}{b}_{jk}.$