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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3 citations
TL;DR: In this paper, the problem of redundancy conditions among the internal coordinates and rows of G-matrix with zero eigenvalues was discussed, in short matrix form, and it was shown that the same relations are satisfied both for the coordinates and Gmatrix rows.
3 citations
TL;DR: In this article, an extrapolated form of the basic first order stationary iterative method for solving linear systems when the associated iteration matrix possesses complex eigenvalues is investigated, and sufficient (and necessary) conditions are given such that convergence is assured.
Abstract: An extrapolated form of the basic first order stationary iterative method for solving linear systems when the associated iteration matrix possesses complex eigenvalues, is investigated. Sufficient (and necessary) conditions are given such that convergence is assured. An analytic determination of good (and sometimes optimum) values of the involved real parameter is presented in terms of certain bounds on the eigenvalues of the iteration matrix. The usefulness of the developed theory is shown through a simple application to the conventional Jacobi method.
3 citations
3 citations
TL;DR: In this paper, it was shown that the determinant of the conductance node matrix of an arbitrary k-loop LC-circuit is the Weinstein function for the loop impendance matrix of this circuit, and vice versa.
Abstract: This work is devoted to the development of a new method for solving the complete generalized problem of large-scale electrical circuit eigenvalues. We prove that the determinant of the conductance node matrix of an arbitrary k-loop LC-circuit is the Weinstein function for the loop impendance matrix of this circuit, and vice versa. A recurrent method of imposing constraints on the basic problem was defined, which permitted us to separate roots of characteristic polynomials in the recurrent process. Also a condition for conservativity of multiple eigenvalues was defined. A solution algorithm for the problem of defining a full range of eigenvalues of an oscillatory system with a finite number of degrees of freedom was suggested.
3 citations