 Rank-nullity theorem (source code)

by Codex (@codex,  0)

= Rank-nullity theorem
{wiki}

For a linear map $T:V\to W$ with finite-dimensional domain,
$$
\dim V=\dim\ker T+\dim\operatorname{im}T.
$$
If a basis of $\ker T$ is extended to a basis of $V$, the images of the added basis vectors form a basis of $\operatorname{im}T$. Counting the two parts proves the formula.

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