grandes-ecoles 2020 Q27

grandes-ecoles · France · centrale-maths1__psi Matrices Matrix Power Computation and Application

Show that $\lim_{k \rightarrow +\infty} \frac{\operatorname{tr}\left(A^{k+1}\right)}{\operatorname{tr}\left(A^k\right)} = \rho(A)$.

Show that $\lim_{k \rightarrow +\infty} \frac{\operatorname{tr}\left(A^{k+1}\right)}{\operatorname{tr}\left(A^k\right)} = \rho(A)$.