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Approximation by matrices with simple spectra

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Abstract

This note deals with a problem on approximation of a matrix tuple by a finite family of diagonalizable matrices with simple eigenvalues. In addition, for a given tuple of matrix functions, it is required that the product of their values at those diagonalizable matrices has a simple spectrum. We solve this problem making use of topological properties of the full matrix algebra.

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Authors and Affiliations

  1. Chair of Mathematical Analysis, Lobachevskii Institute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya 35, Kazan, Tatarstan, 420008, Russia

    R. N. Gumerov & S. I. Vidunov

Authors
  1. R. N. Gumerov
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  2. S. I. Vidunov
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Corresponding authors

Correspondence to R. N. Gumerov or S. I. Vidunov.

Additional information

Submitted by S. A. Grigoryan

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Gumerov, R.N., Vidunov, S.I. Approximation by matrices with simple spectra. Lobachevskii J Math 37, 240–243 (2016). https://doi.org/10.1134/S1995080216030112

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  • DOI: https://doi.org/10.1134/S1995080216030112

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