grandes-ecoles 2020 Q22

grandes-ecoles · France · centrale-maths1__psi Matrices Eigenvalue and Characteristic Polynomial Analysis
Throughout part II, $A \in \mathcal{M}_n(\mathbb{R})$ is a strictly positive matrix satisfying $\rho(A) = 1$. Show that $\dim\left(\ker\left(A - I_n\right)\right) = 1$. 
Throughout part II, $A \in \mathcal{M}_n(\mathbb{R})$ is a strictly positive matrix satisfying $\rho(A) = 1$. Show that $\dim\left(\ker\left(A - I_n\right)\right) = 1$.
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