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

Are the $\lambda_z$ 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 largest eigenvalue is defined as $\lambda_z=\max\{|\lambda|: \lambda \  is \ eigenvalue \}$