The column space of an m-by-n matrix is a subspace of R^m (or C^m)

Created almost 9 years ago, updated about 8 hours ago

For $A\in\mathbb F^{m\times n}$, $\operatorname{Col}(A)$ is a subspace of $\mathbb F^m$. Indeed, if $u=Ax$ and $v=Ay$, then $\alpha u+\beta v=A(\alpha x+\beta y)$. It contains zero by taking $x=0$.

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