### Linear Projection

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**Sun Sep 22, 2019 5:36 pm**Let $\mathcal{V}$ be a linear space over $\mathbb{R}$ such that $\dim_{\mathbb{R}} \mathcal{V} < \infty$ and $f:\mathcal{V} \rightarrow \mathcal{V}$ be a linear projection such that any non zero vector of $\mathcal{V}$ is an eigenvector of $f$. Prove that there exists $\lambda \in \mathbb{R}$ such that $f = \lambda \; \mathrm{Id}$ where $\mathrm{Id}$ is the identity endomorphism.