We define pseudo-reality and pseudo-adjointness of a Hamiltonian, H, as ρHρ−1 = H∗ and μHμ−1 = H ′, respectively. We prove that the former yields the necessary condition for spectrum to be real whereas the latter helps in fixing a definition for inner-product of the eigenstates. Here we separate out adjointness of an operator from its Hermitian-adjointness. It turns out that a Hamiltonian posse...

Let the eigenvalues of a graph and the angles between eigenspaces and the co-ordinate axes of the corresponding real vector space be given for a graph. Cvetković [2] gave a method of constructing a graph which is the supergraph of all graphs with given eigenvalues and angles. Based on this, we describe a branch & bound algorithm for constructing all graphs with given eigenvalues and angles.

Based on Lyapunov-exponent generation and the Gram-Schimdt orthogonalization, analysis and design of some anti-controlled higher-dimensional hyperchaotic systems are investigated in this paper. First, some theoretical results for Lyapunov-exponent generating algorithms are proposed. Then, the relationship between the number of Lyapunov exponents and the number of positive real parts of the eige...

The present paper investigates state space analysis of memristor based series and parallel RLCM circuits. The stability analysis is carried out with the help of eigenvalues formulation method, pole-zero plot and transient response of system. The state space analysis is successfully applied and eigenvalues of the two circuits are calculated. It is found that the, system follows negative real par...

In this paper, a new approach is presented to determine common eigenvalues of two matrices. It is based on Gerschgorin theorem and Bisection method. The proposed approach is simple and can be useful in image processing and noise estimation. KeywordsCommon Eigenvalues, Gerschgorin theorem, Bisection method, real matrices. INTRODUCTION Eigenvalues play vary important role in engineering applicati...

New perturbation results for the behavior of eigenvalues and Jordan forms of real and complex matrices under generic rank one perturbations are discussed. Several results that are available in the complex case are proved as well for the real case and the assumptions on the genericity are weakened. Rank one perturbations that lead to maximal algebraic multiplicities of the “new” eigenvalues are ...

A function F on the space of n × n real symmetric matrices is called spectral if it depends only on the eigenvalues of its argument. Spectral functions are just symmetric functions of the eigenvalues. We show that a spectral function is twice (continuously) differentiable at a matrix if and only if the corresponding symmetric function is twice (continuously) differentiable at the vector of eige...

We study operator Lyapunov equations in which the innnitesimal generator is not necessarily stable; but it satisses a spectrum decomposition assumption and it has at most nitely many unstable eigenvalues. Under mild conditions; these have unique self-adjoint solutions. We give conditions under which the number of negative eigenvalues of this solution equals the number of unstable eigenvalues of...