Let $A(z)$ be a $n\times n$ square matrix depending on the complex value $z$ and $\lambda_z$ is its spectral radius.

Is $\lambda_z$ continous or is it possible that it can jump? Or maybe someone knows a good example for that?

Comment: $A(z)$ consists of complex functions $a_{ij}(z)$ and the spectral radius is defined as $$ \lambda_z=\max\{|\lambda|:\text{ $\lambda$ is an eigenvalue of $A(z)$}\}. $$