Topic
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.
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TL;DR: In this article, the authors consider the problem of finding the spectrum of an n × n matrix, which arises in the study of a certain model of long-range interactions in a one-dimensional statistical mechanics system.
Abstract: We consider the problem of finding the spectrum of an n × n matrix which arises in the study of a certain model of long-range interactions in a one-dimensional statistical mechanics system. Our analysis exhibits a curious resemblance of the suitably normalized distribution of eigenvalues to the Marcenko–Pastur law in the limit n → ∞.
3 citations
TL;DR: The number of independent invariants of n×n matrices A, B and their products on which the eigenvalues λ(μ) of the matrix pencilA+μB depend is determined by means of the theory of algebraic invariants and combinatorial analysis as discussed by the authors.
Abstract: The number of independent invariants ofn×n matricesA, B and their products on which the eigenvalues λ(μ) of the matrix pencilA+μB depend is determined by means of the theory of algebraic invariants and combinatorial analysis. Formulas are displayed for coefficients for the calculation of λ(μ) forn≤5.
3 citations
TL;DR: In this article, a connection between the number of negative eigenvalues, the parameters of the equation and some properties of the domain was established through the correspondence of the eigen values with those of a related Stekloff problem.
Abstract: This paper deals with several eigenvalue problems that have a finite number of negative eigenvalues. A connection is established between the number of negative eigenvalues, the parameters of the equation and some properties of the domain, through the correspondence of the eigenvalues with those of a related Stekloff problem.
3 citations
TL;DR: A variational approach for the spectrum of non-overdamped pencils is used, relying on Krein space techniques and the Ljusternik-Schnirelman theory of critical points of nonlinear functionals to investigate neutral eigenvalues in a mixed spectral zone.
3 citations
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TL;DR: This paper proposes a general framework that covers the existing schemes and reveals that the matrix mismatch leads to a threshold effect caused by "steering vector competition", and finds that, if there are generalized eigenvalues that are infinite, the threshold will increase unboundedly with the interference power.
Abstract: Matrix pair beamformer (MPB) is a blind beamformer. It exploits the temporal structure of the signal of interest (SOI) and applies generalized eigen-decomposition to a covariance matrix pair. Unlike other blind algorithms, it only uses the second order statistics. A key assumption in the previous work is that the two matrices have the same interference statistics. However, this assumption may be invalid in the presence of multipath propagations or certain "smart" jammers, and we call it as matrix mismatch. This paper analyzes the performance of MPB with matrix mismatch. First, we propose a general framework that covers the existing schemes. Then, we derive its normalized output SINR. It reveals that the matrix mismatch leads to a threshold effect caused by "steering vector competition". Second, using matrix perturbation theory, we find that, if there are generalized eigenvalues that are infinite, the threshold will increase unboundedly with the interference power. This is highly probable when there are multiple periodical interferers. Finally, we present simulation results to verify our analysis.
3 citations