grandes-ecoles 2019 Q18

grandes-ecoles · France · centrale-maths2__psi Matrices Eigenvalue and Characteristic Polynomial Analysis
Let $A$ denote a matrix in $\mathcal{M}_n(\mathbb{C})$. Assume that $P$ is an annihilating polynomial of $A$ nilpotent.
Prove that 0 is a root of $P$. 
Let $A$ denote a matrix in $\mathcal{M}_n(\mathbb{C})$. Assume that $P$ is an annihilating polynomial of $A$ nilpotent.

Prove that 0 is a root of $P$.
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