Exceptional Points, Nonnormal Matrices, Hierarchy of Spin Matrices and an Eigenvalue Problem

Exceptional points of a class of non-hermitian Hamilton operators $\widehat{H}$ of the form $\widehat{H}={\widehat{H}}_0+i{\widehat{H}}_1$ are studied, where ${\widehat{H}}_0$ and $\hat H_1$ are hermitian operators. Finite dimensional Hilbert spaces are considered. The linear operators ${\widehat{H}}_0$ and ${\widehat{H}}_1$ are given by spin matrices for spin $s=1\mathrm{/}2,1,3\mathrm{/}2,\dots$. Since the linear operators studied are nonnormal, properties of such operators are described.