rank–nullity theorem

《Algebraic and Analytic Geometry》 · 第 70 页 · Section 2.1「Linear Transformations, Null Spaces, and Ranges」，Theorem 2.3

Let $V$ and $W$ be vector spaces, and let $T:V\to W$ be linear. If $V$ is finite-dimensional, then $\operatorname{nullity}(T)+\operatorname{rank}(T)=\dim(V)$.