grandes-ecoles 2020 Q19

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 $\rho(A) = 1$. We consider an eigenvalue $\lambda \in \mathbb{C}$ of $A$ with modulus 1 and $x$ an eigenvector associated with $\lambda$. Conclude (that 1 is an eigenvalue of $A$). 
Throughout part II, $A \in \mathcal{M}_n(\mathbb{R})$ is a strictly positive matrix satisfying $\rho(A) = 1$. We consider an eigenvalue $\lambda \in \mathbb{C}$ of $A$ with modulus 1 and $x$ an eigenvector associated with $\lambda$. Conclude (that 1 is an eigenvalue of $A$).
Paper Questions
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