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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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Journal ArticleDOI
01 Jul 1991
TL;DR: In this article, an optimal controller with prescribed dominant energy eigenvalues is proposed, which can be used for efficiently tuning the weighting matrix of an already optimal feedback system so that the dominant eigen values of the resulting system are located in the desired region.
Abstract: An optimal controller with prescribed dominant energy eigenvalues is proposed. The closed-loop control system preserves some of the eigenvalues of the original system. The eigenvalues selected to shift into the desired region are determined using the concept of dominant energy modes. A systematic design method, for sequentially finding the weighting matrix elements and the feedback gains of the controller corresponding to the given eigenvalues, is developed. The proposed method can also be used for efficiently tuning the weighting matrix of an already optimal feedback system so that the dominant eigenvalues of the resulting system are located in the desired region. It follows that, by shifting only the dominant eigenvalues of the proposed controller, simple and efficient control of the dynamic system can be obtained. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

4 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider the self-adjoint operator of a generalized Friedrichs model whose essential spectrum may contain lacunas and obtain a formula for the number of eigenvalues lying on an arbitrary interval outside the essential spectrum.
Abstract: We consider the self-adjoint operator of a generalized Friedrichs model whose essential spectrum may contain lacunas. We obtain a formula for the number of eigenvalues lying on an arbitrary interval outside the essential spectrum of this operator. We find a sufficient condition for the discrete spectrum to be finite. Applying the formula for the number of eigenvalues, we show that there exist an infinite number of eigenvalues on the lacuna for a particular Friedrichs model and obtain the asymptotics for the number of eigenvalues.

4 citations

Journal ArticleDOI
TL;DR: This paper corrected an error in the results of Subsection 3.1 in authors' paper "On Eigenvalues of Laplacian Matrix for a Class of Directed Signed Graphs" which appeared in Linear Algebra and its Applications 523 (2017), 281−306.

4 citations

Journal ArticleDOI
TL;DR: In this paper, the eigenvalues of the Hamiltonian matrix in a finite basis spanning the inner configuration space are used to generate a set of accurate values of the S-matrix at these eigenenergies.
Abstract: We show that, in the context of the R-matrix method, the eigenvalues of the Hamiltonian matrix in a finite basis spanning the inner configuration space can be used to generate a set of accurate values of the S-matrix at these eigenenergies. This set is then used as input in an analytic continuation scheme to locate several resonances accurately in the complex energy plane.

4 citations

Book ChapterDOI
01 Jan 2009
TL;DR: In this paper, the eigenvalues of a compression of a monic quadratic weakly hyperbolic polynomial to an (n − 1)-dimensional subspace of ℂ n block-interlace were proved.
Abstract: Let L be a monic quadratic weakly hyperbolic or hyperbolic n × n matrix polynomial. We solve some direct spectral problems: We prove that the eigenvalues of a compression of L to an (n − 1)-dimensional subspace of ℂ n block-interlace and that the eigenvalues of a one-dimensional perturbation of L (−,+)-interlace the eigenvalues of L. We also solve an inverse spectral problem: We identify two given block-interlacing sets of real numbers as the sets of eigenvalues of L and its compression.

4 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20238
20229
20202
20193
20187
201731