Exercise31.2
Use the existance of the Schur Form of the matrix \(A \in \Cmm\) to prove that \[ \lim_{n \to \infty} \|A^n\| = 0 \iff \rho(A) \lt 1, \] where \(\rho(A)\) is the spectral radius of \(A\text{.}\)
Use the existance of the Schur Form of the matrix \(A \in \Cmm\) to prove that \[ \lim_{n \to \infty} \|A^n\| = 0 \iff \rho(A) \lt 1, \] where \(\rho(A)\) is the spectral radius of \(A\text{.}\)