Three equivalent formulas describe matrix multiplication: $(AB)_{ij}=\sum_k a_{ik}b_{kj}$; the $j$th column is $Ab_j$; and $AB=\sum_k a_k r_k$, where $a_k$ is column $k$ of $A$ and $r_k$ is row $k$ of $B$. The last expression is a sum of rank-at-most-one outer products.
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