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On the 2-norm distance from a normal matrix to the set of matrices with a multiple zero eigenvalue

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Abstract

An elementary proof of a formula for the 2-norm distance from a normal matrix A to the set of matrices with a multiple zero eigenvalue is given. Earlier, the authors obtained this formula as an implication of a nontrivial result due to A. N. Malyshev. Bibliography: 4 titles.

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References

  1. A. N. Malyshev, “A formula for the 2-norm distance from a matrix to the set of matrices with multiple eigenvalues,” Numer. Math., 83, 443–454 (1999).

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  2. Kh. D. Ikramov and A. M. Nazari, “On a remarkable implication of the Malyshev formula,” Dokl. Akad. Nauk, 385, 599–600 (2002).

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  3. Kh. D. Ikramov, “Explicit formulas for the matrix with a multiple zero eigenvalue closest to a given normal matrix,” Dokl. Akad. Nauk, 398, 599–601 (2004).

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  4. C. Eckart and G. Young, “The approximation of one matrix by another of lower rank,” Psychometrica, 1, 211–218 (1936).

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    Kh. D. Ikramov & A. M. Nazari

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  1. Kh. D. Ikramov
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  2. A. M. Nazari
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 50–56.

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Ikramov, K.D., Nazari, A.M. On the 2-norm distance from a normal matrix to the set of matrices with a multiple zero eigenvalue. J Math Sci 137, 4789–4793 (2006). https://doi.org/10.1007/s10958-006-0277-5

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  • DOI: https://doi.org/10.1007/s10958-006-0277-5

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