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**FernandoRevilla** Perhaps you mean: if $\displaystyle T:V\to V$ is an endomorphism, $\displaystyle \dim V=n$ and $\displaystyle W$ a subspace of $\displaystyle V$ with $\displaystyle T(W)\subseteq W$ then, there exists a basis $\displaystyle B$ of $\displaystyle V$ such that $\displaystyle [T]_B=\begin{bmatrix}{A}&{C}\\{0}&{D}\end{bmatrix}$ . If this is the case, then choose $\displaystyle B=\{e_1,\ldots,e_r,e_{r+1},\ldots,e_n\}$ where $\displaystyle \{e_1,\ldots,e_r\}$ is a basis of $\displaystyle W$ . You'll easily find $\displaystyle [T]_B$ .