We present a classification of non-hermitian random matrices based on implementing commuting discrete symmetries. It contains 43 classes. This generalizes the classification of hermitian random matrices due to Altland-Zirnbauer and it also extends the Ginibre ensembles of nonhermitian matrices [1]. Random matrix theory originates from the work of Wigner and Dyson on random hamiltonians [2]. Sin...

While there is no lack of efficient Krylov subspace solvers for Hermitian systems, few exist for complex symmetric, skew symmetric, or skew Hermitian systems, which are increasingly important in modern applications including quantum dynamics, electromagnetics, and power systems. For a large, consistent, complex symmetric system, one may apply a non-Hermitian Krylov subspace method disregarding ...

In this note we characterize polynomial numerical hulls of matrices $A in M_n$ such that$A^2$ is Hermitian. Also, we consider normal matrices $A in M_n$ whose $k^{th}$ power are semidefinite. For such matriceswe show that $V^k(A)=sigma(A)$.

the paper deal with non-commutative geometry. the notion of quantumspheres was introduced by podles. here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.

in this paper, an iterative method is proposed for solving the matrix inverse problem $ax=b$ for hermitian-generalized hamiltonian matrices with a submatrix constraint. by this iterative method, for any initial matrix $a_0$, a solution $a^*$ can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of...

We study the quantum entanglement and separability of Hermitian and pseudo-Hermitian systems of identical bosonic or fermionic particles with point interactions. The separability conditions are investigated in detail. PACS numbers: 02.30.Ik, 11.30.Er, 03.65.Fd

The Hermitian and skew-Hermitian parts of a square matrix A are deened by H(A) (A + A)=2 and S(A) (A ? A)=2: We show that the function f(A) = (H(A ?1)) ?1 is convex with respect to the Loewner partial order on the cone of matrices with positive deenite Hermitian part. That is, for any matrices A and B with positive deenite Hermitian part ff(A) + f(B)g=2 ? f(fA + Bg=2) is positive semideenite: U...

We show that a quantum system possessing an exact antilinear symmetry, in particular PT -symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct the unitary operator relating an arbitrary non-Hermitian Hamiltonian with exact PT -symmetry to a Hermitian Hamiltonian. We apply our general results to PT symmetry in finite-dimensions and give the explicit form of the...

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP are the generic members in this family; the remaining spaces are some contractions of the former. The method encapsulates trigonometry for this whole family of spaces into a single ba...