A non-Hermitian complex symmetric 2 × 2-matrix toy model is used to study projective Hilbert space structures in the vicinity of exceptional points (EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are Puiseuxexpanded in terms of the root vectors at the EP. It is shown that the apparent contradiction between the two incompatible normalization conditions with finite and singular b...

In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are  generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.

We consider the random matrix ensemble with an external source 1 Zn e−nTr( 1 2M −AM)dM defined on n×n Hermitian matrices, where A is a diagonal matrix with only two eigenvalues ±a of equal multiplicity. For the case a > 1, we establish the universal behavior of local eigenvalue correlations in the limit n → ∞, which is known from unitarily invariant random matrix models. Thus, local eigenvalue ...

It has been shown by Strahov and Fyodorov that averages of products and ratios of characteristic polynomials corresponding to Hermitian matrices of a unitary ensemble, involve kernels related to orthogonal polynomials and their Cauchy transforms. We will show that, for the unitary ensemble 1 Ẑn | detM |2αe−nV dM of n×n Hermitian matrices, these kernels have universal behavior at the origin of t...

In the paper we consider a matrix version of the extremal Nehary problem [1],[4]. Our approach is based on the notion of a matrix analogue of the eigenvalue ρ2min. The notion of ρ 2 min was used in a number of the extremal interpolation problems [2],[3],[7]. We note that ρ2min is a solution of a nonlinear matrix inequality of the Riccati type [2],[6], [7]. Our approach coincides with the Adamja...