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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10 Dec 1997TL;DR: In this article, the eigenvalues problem of matrix A+B has been studied and several relationships among the Eigenvalues of matrices A, B, A and B are proposed.
Abstract: This paper deals with the eigenvalues problem of matrix A+B. Several relationships among the eigenvalues of matrices A, B and A+B are proposed. Some simplified formulas for the eigenvalues of low order matrices are also proposed. These results are applied to the robustness analysis of uncertain state space systems.
2 citations
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TL;DR: In this article, a numerical method is developed for the evaluation of the eigenvalues and eigenfunctions of continuous systems, based on the possibility of producing linearly independent numerical complementary integrals of the R th order ordinary differential equations by integrating the same R times with starting values having non-zero Wronskian.
Abstract: The general definition of the eigenvalue problems of continuous systems is briefly discussed. The conventional method of solution is outlined up to the degree necessary for the understanding of the proposed numerical method. The numerical method is developed for the evaluation of the eigenvalues and eigenfunctions. This method is based on the possibility of producing linearly independent numerical complementary integrals of the R th order ordinary differential equations by integrating the same R times with starting values having non-zero Wronskian. The eigenvalues are obtained by “hunting” for the zeros of the matrix of coefficients of the integration constants obtained from the homogeneous boundary conditions of the eigenvalue problem. Any degree of accuracy can be achieved and the accuracy of higher eigenvalues does not depend on the accuracy of lower eigenvalues. Numerical method is applied to two sample problems. The second of these samples treats a problem that has been solved previously in an approximate manner.
2 citations
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31 Mar 2017TL;DR: In this article, the authors studied the spectrum of unbounded J-self-adjoint block operator matrices and proved enclosures for the spectrum and derived variational principles for certain real eigenvalues even in the presence of non-real spectrum.
Abstract: We study the spectrum of unbounded J-self-adjoint block operator matrices. In particular, we prove enclosures for the spectrum, provide a sufficient condition for the spectrum being real and derive variational principles for certain real eigenvalues even in the presence of non-real spectrum. The latter lead to lower and upper bounds and asymptotic estimates for eigenvalues.
2 citations
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TL;DR: In this paper, the authors considered self-adjoint boundary value problems with discrete spectrum and coefficients periodic in a certain coordinate and established upper bounds for eigenvalues in terms of the eigen values of the corresponding problem with averaged coefficients.
Abstract: We consider self-adjoint boundary-value problems with discrete spectrum and coefficients periodic in a certain coordinate. We establish upper bounds for eigenvalues in terms of the eigenvalues of the corresponding problem with averaged coefficients. We illustrate the results obtained in the case of the Hill vector equation and for circular and rectangular plates with periodic coefficients.
2 citations