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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
TL;DR: This algorithm can be used for computing the eigenvalues of all kind of singular systems and for identifying whether signular systems have impulsive motions and the finite fixed modes.
01 Jan 2015
TL;DR: In this paper, it was shown that B2n has exactly one positive real eigenvalue and onenegative real eigvalue and, as aby-product,reprovethateveryBrualdi-Li matrix has distinct eigenvalues.
Abstract: Inthispaperwederivenewpropertiescomplementarytoan2n×2nBrualdi-Li tournament matrix B2n. We show that B2n has exactly one positive real eigenvalue and onenegative real eigenvalue and, as aby-product,reprovethateveryBrualdi-Li matrix has distinct eigenvalues. We then bound the partial sums of the real parts and the imaginary parts of its eigenvalues. The inverse of B2nis also determined. Related results obtained in previous articles are proven to be corollaries.
Journal ArticleDOI
TL;DR: In this paper, the authors proved that the number of positive eigenvalues of the solution is equal to the rank of the controllability matrix formed from the coefficient matrices.
Abstract: It is known that the discrete Lyapunov matrix equation has a positive semidefinite symmetric solution under an appropriate condition. This note proves the fact that the number of positive eigenvalues of the solution is equal to the rank of the controllability matrix formed from the coefficient matrices.
Journal ArticleDOI
TL;DR: The framework for accelerated spectral refinement for a simple eigenvalue developed in Part I of this paper is employed to treat the general case of a cluster of eigenvalues whose total algebraic multiplicity is finite.
Abstract: The framework for accelerated spectral refinement for a simple eigenvalue developed in Part I of this paper is employed to treat the general case of a cluster of eigenvalues whose total algebraic multiplicity is finite. Numerical examples concerning the largest and the second largest multiple eigenvalues of an integral operator are given.

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