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We explore the concept of eigenvalue avoidance, which is well understood for real symmetric and Hermitian matrices, for other classes of structured matrices. We adopt a differential geometric perspective and study the generic behaviour of…
Racah matrices of quantum algebras are of great interest at present time. These matrices have a relation with $\mathcal{R}$-matrices, which are much simpler than the Racah matrices themselves. This relation is known as the eigenvalue…
We study the transient heat current out of a confined electron system into a weakly coupled electrode in response to a voltage switch. We show that the decay of the Coulomb interaction energy for this repulsive system exhibits signatures of…
We present a kind of construction for a class of special matrices with at most two different eigenvalues, in terms of some interesting multiplicators which are very useful in calculating eigenvalue polynomials of these matrices. This class…
Eigenvalues of a density matrix characterize well the quantum state's properties, such as coherence and entanglement. We propose a simple method to determine all the eigenvalues of an unknown density matrix of a finite-dimensional system in…
In this paper we are concerned to find the eigenvalues and eigenvectors of a real symetric matrix by applying a new numerical method similar to Jacobi method. Our approch consists to use a new orthogonal matrix. The computation of the…
A remarkable mathematical property -- somehow hidden and recently rediscovered -- allows obtaining the eigenvectors of a Hermitian matrix directly from their eigenvalues. That opens the possibility to get the wavefunctions from the…
What is the connection of random matrices with integrable systems? Is this connection really useful? Introducing apprpriate times in the distribution of the ensemble of matrices, one shows that the corresponding distribution of the…
We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.
It is an established fact that quantum coherences have thermodynamic value. The natural question arises, whether other genuine quantum properties such as entanglement can also be exploited to extract thermodynamic work. In the present…
The fact that the capacitance coefficients for a set of conductors are geometrical factors is derived in most electricity and magnetism textbooks. We present an alternative derivation based on Laplace's equation that is accessible for an…
Reciprocity is shown so far only when the scattering potential is either real or parity symmetric complex. We extend this result for parity violating complex potential by considering several explicit examples: (i) we show reciprocity for a…
We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as…
For two real symmetric matrices, their eigenvalue configuration is therelative arrangement of their eigenvalues on the real line. We consider the following problem: given two parametric real symmetric matrices and an eigenvalue…
The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each…
We prove that the matrix of capacitance in electrostatics is a positive-singular matrix with a non-degenerate null eigenvalue. We explore the physical implications of this fact, and study the physical meaning of the eigenvalue problem for…
This note deals with a simultaneous approximation of several matrices by a finite family of diagonalizable matrices satisfying an additional condition for the spectrum of a matrix product. That is the simplicity of all eigenvalues.
This paper presents an overview of the derivation and significance of recently derived conservation laws for the matrix moments of Hermitean random matrices with dominant exponential weights that may be either even or odd. This is based on…
The entanglement content of superpositions of pairs of degenerate eigenstates of a bipartite system are considered in the case that both are also eigenstates of the $z$ component of the total angular momentum. It is shown that the von…
The inverse eigenvalue problem studies the possible spectra among matrices whose off-diagonal entries have their zero-nonzero patterns described by the adjacency of a graph $G$. In this paper, we refer to the $i$-nullity pair of a matrix…