Kestenband proved in [12] that there are only seven pairwise non-isomorphic Hermitian intersections in the desarguesian projective plane PG…2; q† of square order q. His classi®cation is based on the study of the minimal polynomials of the matrices associated with the curves and leads to results of purely combinatorial nature: in fact, two Hermitian intersections from the same class might not be...

The extreme ranks, i.e., the maximal and minimal ranks, are established for the general Hermitian solution as well as the general skew-Hermitian solution to the classical matrix equation AXA +BY B = C over the quaternion algebra. Also given in this paper are the formulas of extreme ranks of real matrices Xi, Yi, i = 1, · · · , 4, in a pair (skew-)Hermitian solution X = X1 + X2i + X3j + X4k, Y =...

We give in this paper some closed-form formulas for the maximal and minimal values of the rank and inertia of the Hermitian matrix expression A − BX ± (BX)∗ with respect to a variable matrix X. As applications, we derive the extremal values of the ranks/inertias of the matrices X and X ± X∗, where X is a (Hermitian) solution to the matrix equation AXB = C, respectively, and give necessary and s...

In recent years, non-Hermitian quantum physics has gained a lot in popularity the optics and condensed matter communities order to model systems with varying symmetries. this paper, we identify non-standard inner product that implies bosonic commutator relations for local electric magnetic field observables leads natural biorthogonal description of quantised electromagnetic field. When comparin...

We study non-Hermitian quantummechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in both the cases are found to be real. It is also shown that the models are η pseudo-Hermitian and the metric operator is found explicitly in both the cases.