Spectral Properties of Pseudo-Hermitian Matrices

The statistical properties of the eigenvalues of pseudo-Hermitian random matrices whose eigenvalues are real or complex conjugate are investigated. It is shown that when the spectrum splits into separated sets of real and complex conjugate eigenvalues, the real ones show characteristics of an intermediate incomplete spectrum, that is, of a so-called thinned ensemble. On the other hand, the complex ones show repulsion compatible with cubic-order repulsion of non-normal matrices for the real matrices, but higher-order repulsion for the complex and quaternion matrices.