A class of spherically symmetric non-Hermitian Hamiltonians and their η-pseudo-Hermiticity generators are presented. An operators-based procedure is introduced so that the results for the 1D Schrödinger Hamiltonian may very well be reproduced. A generalization beyond the nodeless states is proposed. Our illustrative examples include η-pseudo-Hermiticity generators for the non-Hermitian weakly p...

Interior point methods can be extended to a number of cones (self-dual homogeneous cones) • Rn (linear programming) • vectorized symmetric matrices over real numbers (semidefinite programming) • vectorized Hermitian matrices over complex numbers • vectorized Hermitian matrices over quaternions • vectorized Hermitian 3×3 matrices over octonions Grötschel, Lovász and Schrijver [3]: semidefinite p...

Exact solvability of some non-Hermitian η-weak-pseudo-Hermitian Hamiltonians is explored as a byproduct of η-weak-pseudo-Hermiticity generators. A class of Veff (x) = V (x) + iW (x) potentials is considered, where the imaginary part W (x) is used as an η-weak-pseudo-Hermiticity generator to obtain exactly solvable η-weak-pseudo-Hermitian Hamiltonian models. PACS numbers: 03.65.Ge, 03.65.Fd,03.6...

The computation of eigenvalues and eigenvectors of matrix polynomials is an important, but di cult, problem. The standard approach to solve this problem is to use linearizations, which are matrix polynomials of degree 1 that share the eigenvalues of P ( ). Hermitian matrix polynomials and their real eigenvalues are of particular interest in applications. Attached to these eigenvalues is a set o...

1 Hermitian eigenvalue problem For any n × n Hermitian matrix A, let λA = (λ1 ≥ · · · ≥ λn) be its set of eigenvalues written in descending order. (Recall that all the eigenvalues of a Hermitian matrix are real.) We recall the following classical problem. Problem 1. (The Hermitian eigenvalue problem) Given two n-tuples of nonincreasing real numbers: λ = (λ1 ≥ · · · ≥ λn) and μ = (μ1 ≥ · · · ≥ μ...

We study analogues of classical inequalities for the eigenvalues of sums of Hermitian matrices for the cone of admissible elements in the pseudo-Hermitian case. In particular, we obtain analogues of the Lidskii-Wielandt inequalities.

We study 2-incompressible Grassmannians of isotropic subspaces of a quadratic form, of a hermitian form over a quadratic extension of the base field, and of a hermitian form over a quaternion algebra.

We prove a convergence result for an iterative method, proposed recently by B. Meini, for finding the maximal Hermitian positive definite solution of the matrix equationX+A∗X−1A = Q, where Q is Hermitian positive definite.