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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: In this article, a single-input modal control theory is developed whereby the loop gains of a time-invariant multi-variable system may be calculated using simple formulae for the cases when both the open-loop plant matrix and the closed-loop plants matrix have a number of distinct and confluent eigenvalues.
Abstract: A single-input modal control theory is developed whereby the loop gains of a single-input time-invariant multi-variable system may be calculated using simple formulae for the cases when both the open-loop plant matrix and the closed-loop plant matrix have a number of sets of distinct and confluent eigenvalues. The results may be applied in a sequential manner for multi-input systems with repeated sets of confluent eigenvalues provided that the appropriate mode-controllability conditions are satisfied. A number of illustrative examples are included.

5 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a method to determine explicitly whether a given system has only eigenvalues with negative real parts, without determining these eigen values, but rather by determining the eigen value of a related symmetric matrix which are always real and hence easy to calculate.
Abstract: The method introduced here determines explicitly whether a given system has only eigenvalues with negative real parts, without determining these eigenvalues, but rather by determining the eigenvalues of a related symmetric matrix which are always real and hence easy to calculate. The new method is similarly applied to linear autonomous discrete systems where all the eigenvalues of the system matrix are required to be positioned within the unit circle in the z-plane.

5 citations

Journal ArticleDOI
TL;DR: In this paper, the eigenvalues of a square quaternion matrix have been studied by considering the equation Gy = μ ǫ, where G is an n x n complex matrix, y is a non-zero vector in Cn, μ is a complex number, and ȳ is the conjugate of y.
Abstract: The nature of the eigenvalues of a square quaternion matrix had been considered by Lee [1] and Brenner [2]. In this paper the author gives another elementary proof of the theorems on the eigenvalues of a square quaternion matrix by considering the equation Gy = μȳ, where G is an n x n complex matrix, y is a non-zero vector in Cn, μ is a complex number, and ȳ is the conjugate of y. The author wishes to thank Professor Y. C. Wong for his supervision during the preparation of this paper.

5 citations

Journal ArticleDOI
TL;DR: In this article, an algebraic theorem concerning the separation of the eigenvalues of a matrix is discussed for degenerate eigen values in variation calculations, and it is shown that the occurrence of degenerate values in a given approximation does not prevent the application of the theorem to the determination of upper bounds for exact eigen value in physical problems.
Abstract: An algebraic theorem concerning the separation of the eigenvalues of a matrix is discussed for degenerate eigenvalues in variation calculations. It is shown that the occurrence of degenerate eigenvalues in a given approximation does not prevent the application of the theorem to the determination of upper bounds for exact eigenvalues in physical problems.

5 citations

Journal ArticleDOI
Abstract: This paper is a continuation of our recent work on the localization of the eigenvalues of matrices. We give new bounds for the real and imaginary parts of the eigenvalues of matrices. Applications to the localization of the zeros of polynomials are also given.

5 citations


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