Source: /cirosantilli/matrix-multiplication

= Matrix multiplication
{wiki}

= Matrix product
{synonym}

Since a <matrix> $M$ can be seen as a <linear map> $f_M(\vec{x})$, the product of two matrices $MN$ can be seen as the composition of two <linear maps>:
$$
f_M(f_N(\vec{x}))
$$
One cool thing about linear functions is that we can easily pre-calculate this product only once to obtain a new matrix, and so we don't have to do both multiplications separately each time.