grandes-ecoles 2010 QIIIA2

grandes-ecoles · France · centrale-maths2__pc Invariant lines and eigenvalues and vectors Invariant subspaces and stable subspace analysis

Let $V$ be a $\mathbb { K }$-vector space of finite non-zero dimension. Let $f$ and $g$ be two endomorphisms of $V$ that commute, that is, such that $f \circ g = g \circ f$. Show that the eigenspaces of $f$ are stable under $g$.

Let $V$ be a $\mathbb { K }$-vector space of finite non-zero dimension. Let $f$ and $g$ be two endomorphisms of $V$ that commute, that is, such that $f \circ g = g \circ f$. Show that the eigenspaces of $f$ are stable under $g$.

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