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

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