Vanesa Cortés, Juan Peña, Tomas Sauer (2012)
Open Mathematics
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We present an extension of the QR method to simultaneously compute the joint eigenvalues of a finite family of commuting matrices. The problem is motivated by the task of finding solutions of a polynomial system. Several examples are included.
R. Zezula, J. Roček, A. Miasnikov (1977)
Acta Universitatis Carolinae. Mathematica et Physica
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Rafael Bru, Rafael Cantó, Ricardo Soto, Ana Urbano (2012)
Open Mathematics
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Given a square matrix A, a Brauer’s theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75–91] shows how to modify one single eigenvalue of A via a rank-one perturbation without changing any of the remaining eigenvalues. Older and newer results can be considered in the framework of the above theorem. In this paper, we present its application to stabilization of control systems, including the case when...
Werner Gautschi (1954-1956)
Compositio Mathematica
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Yeong-Jeu Sun (2003)
Control and Cybernetics
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Guang-Da Hu, Qiao Zhu (2010)
Kybernetika
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This paper is concerned with bounds of eigenvalues of a complex matrix. Both lower and upper bounds of modulus of eigenvalues are given by the Stein equation. Furthermore, two sequences are presented which converge to the minimal and the maximal modulus of eigenvalues, respectively. We have to point out that the two sequences are not recommendable for practical use for finding the minimal and the maximal modulus of eigenvalues.
Meenakshi, Ar., Anandam, N. (1992)
International Journal of Mathematics and Mathematical Sciences
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