Matrix multiplication can be viewed as the dot product of a row vector of column vectors with a column vector of row vectors

Write $A=[a_1\ \cdots\ a_n]$ by columns and write $B$ by rows $r_1,\ldots,r_n$. Then $AB=\sum_{k=1}^n a_kr_k$, a sum of outer products. Entry $ij$ is $\sum_k(a_k)_i(r_k)_j=\sum_k a_{ik}b_{kj}$. This is a block-level row-by-column rule.Copy