is it true that the operator norm of a matrix $A$ is smaller than 1 if its spectral radius $\rho(A)$ is smaller than 1?
many thanks for any help, it is much appreciated!
is it true that the operator norm of a matrix $A$ is smaller than 1 if its spectral radius $\rho(A)$ is smaller than 1?
many thanks for any help, it is much appreciated!
No. Consider for example $ \begin{bmatrix}0&2\\0&0\end{bmatrix}. $ Its spectral radius is $0$, and its operator norm is $2$.
Now, for normal operators, the operator norm and the spectral radius agree.