grandes-ecoles 2010 QIIIA1

grandes-ecoles · France · centrale-maths2__pc Matrices Diagonalizability and Similarity

Let $V$ be a $\mathbb { K }$-vector space of finite non-zero dimension. Let $f$ be a diagonalizable endomorphism of $V$ and $W$ a non-zero subspace of $V$ stable under $f$. Show that the endomorphism of $W$ induced by $f$ is diagonalizable.

Let $V$ be a $\mathbb { K }$-vector space of finite non-zero dimension. Let $f$ be a diagonalizable endomorphism of $V$ and $W$ a non-zero subspace of $V$ stable under $f$. Show that the endomorphism of $W$ induced by $f$ is diagonalizable.

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