We describe a new extension to ScaLAPACK [2] for computing with symmetric (Hermi-tian) matrices stored in a packed form. The new code is built upon the ScaLAPACK routines for full dense storage for a high degree of software reuse. The original ScaLAPACK stores a symmetric matrix as a full matrix but accesses only the lower or upper triangular part. The new code enables more efficient use of mem...

We give a simple proof of the fact that every diagonalizable operator that has a real spectrum is quasi-Hermitian and show how the metric operators associated with a quasiHermitian Hamiltonian are related to the symmetry generators of an equivalent Hermitian Hamiltonian. PACS number: 03.65.-w

We consider a Hamiltonian H = H0 + V , in which H0 is a given nonrandom Hermitian matrix, and V is an N × N Hermitian random matrix with a Gaussian probability distribution. We had shown before that Dyson’s universality of the short-range correlations between energy levels holds at generic points of the spectrum independently of H0. We consider here the case in which the spectrum of H0 is such ...

In this article we consider the system of operator equations T_iX=U_i for i=1,2,...,n and give necessary and suffcient conditions for the existence of common Hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. Also we study the Moore-penrose inverse of a ncross 1 block operator matrix and. then gi...

In this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the Hermitian matrix expression $$‎ ‎f(X,Y)=C_{4}-B_{4}Y-(B_{4}Y)^{*}-A_{4}XA_{4}^{*},$$ where $C_{4}$ is‎ ‎Hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$X$ and $Y$ satisfy‎ ‎the following consistent system of matrix equations $A_{3}Y=C_{3}‎, ‎A_{1}X=C_{1},XB_{1}=D_{1},A_{2}XA_{2}^{*}=C_{2},X=X^{*}.$ As‎ ‎consequences‎, ‎we g...

Structured rational matrices such as symmetric, skew-symmetric, Hamiltonian, skew-Hamiltonian, Hermitian, and para-Hermitian arise in many applications. Linearizations of rational...

was introduced in [2, 3, 6] as a generalization of the coupled quantized harmonic oscillators [7], namely, themodel of light amplifier L−2 1 , and themodel of two-level optical atom L1, whose Hamiltonian model H = K0 +λ(K+ +K−), λ is the coupling parameter. The matrix representations of Lr of least degree satisfying the physical properties K2 =K† 1 († stands for Hermitian conjugation and K0 is ...

For a given standard Hamiltonian H with arbitrary complex scalar and vector potentials in one-dimension, we construct an invertible antilinear operator τ such that H is τ -anti-pseudo-Hermitian, i.e., H = τHτ−1. We use this result to give the explicit form of a linear Hermitian invertible operator with respect to which any standard PT symmetric Hamiltonian with a real degree of freedom is pseud...

In this note, generalized connections σT,f are investigated, where AσT,fB = TAfT − A (B) for positive semidefinite matrix A and hermitian matrix B, and operator monotone function f : J → R on an interval J ⊂ R. Here the symbol T A denotes a reflexive generalized inverse of a positive bounded linear operator TA. The problem of estimating a given generalized connection by other ones is studied. T...

Matrix String Theory of Banks, Fischler, Shenker and Susskind can be understood as a generalized quantum theory (provisionally named " quansical " theory) which differs from Adler's generalized trace quantum dynamics. The effective planar Matrix String Theory Hamiltonian is constructed in a particular fermionic realization of Matrix String Theory treated as an example of " quansical " theory.