Spectrum of a matrix

About: Spectrum of a matrix is a research topic. Over the lifetime, 1064 publications have been published within this topic receiving 19841 citations. The topic is also known as: matrix spectrum.

A note on a distance bound using eigenvalues of the normalized Laplacian matrix

Abstract: Let G be a connected graph, and let X and Y be subsets of its vertex set. A previously published bound is considered that relates the distance between X and Y to the eigenvalues of the normalized Laplacian matrix for G ,t he volumes ofX and Y , and the volumes of their complements. A counterexample is given to the bound, and then a corrected version of the bound is provided.

Matrix models as hidden variables theories

Abstract: It is proposed that the CH−dWHN−BFSS matrix model may be interpreted as non-local hidden variables theories in which the quantum observables are the eigenvalues of the matrices while their entries are the hidden variables. This is shown by studying the matrix model at finite temperature, with T taken to scale as 1/N. For large but finite N the eigenvalues of the matrices undergo Brownian motion around the N→∞ limit, with diffusion constant of order 1/N. The resulting probability density and current for the eigenvalues are then found to evolve in agreement with the Schroedinger equation, to leading order in 1/N, with ℏ proportional to the thermal diffusion constant for the matrix elements. The quantum fluctuations and uncertainties in the positions of the eigenvalues are then consequences of ordinary statistical fluctuations in the values of the matrix elements. The derivation makes use of Nelson’s stochastic formulation of quantum theory, which is expressed in terms of a variational principle.

Spectral deconvolution of unitarily invariant matrix models

Abstract: The present paper implements a complex analytic method to recover the spectrum of a matrix perturbed by either the addition or the multiplication of a random matrix noise, under the assumption that the distribution of the noise is unitarily invariant. This method, introduced by Arizmendi, Tarrago and Vargas in arXiv:1711.08871, is done in two steps : the first step consists in a fixed point method to compute the Stieltjes transform of the desired distribution in a certain domain, and the second step is a classical deconvolution by a Cauchy distribution, whose parameter depends on the intensity of the noise. We also provide explicit bounds for the mean squared error of the first step.

Existence of infinitely many complex eigenvalues for the mono-energetic neutron transport operator

Abstract: In this Letter it is proved that the mono-energetic neutron transport operator for the case of a spherically-symmetric, isotropically-scattering sphere with a central cavity, has infinitely many complex eigenvalues.

Sensitivity functions of distributed-parameter eigenvalue control systems

Abstract: For a class of linear distributed-parameter systems formulas and procedures are given by which one can compute the 1st-and 2nd-order sensitivity functions of the state feedback gain, which moves the system eigenvalues to desired positions, to variations of the system parameters. Analogous results are derived for the sensitivities of the closed-loop eigenvalues.