Definition of matrix multiplication in terms of column vectors

Created almost 9 years ago, updated about 8 hours ago

If $B=[b_1\ \cdots\ b_p]$ and $A$ has as many columns as $B$ has rows, define $AB=[Ab_1\ \cdots\ Ab_p]$. Thus each product column is a linear combination of $A$'s columns. This definition immediately gives $\operatorname{Col}(AB)\subseteq\operatorname{Col}(A)$.

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