We now show how the parallel matrix-vector multiplication
and rank-1 update can be used to implement matrix-matrix multiplication
and other matrix-matrix operations.
For simplicity, we concentrate on the case
*C* = *A B* , where all three matrices are .
In all our explanations, we will use the following partitionings:

with and
where represents the *j* th column of matrix *X* .
Also,

where represents the *i* th row of matrix *X* .