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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 1, Pages 4–7 (Mi zvmmf9632)  

This article is cited in 2 scientific papers (total in 2 papers)

Takagis decomposition of a symmetric unitary matrix as a finite algorithm

Kh. D. Ikramov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992 Russia

Abstract: Takagis decomposition is an analog (for complex symmetric matrices and for unitary similarities replaced by unitary congruences) of the eigenvalue decomposition of Hermitian matrices. It is shown that, if a complex matrix is not only symmetric but is also unitary, then its Takagi decomposition can be found by quadratic radicals, that is, by means of a finite algorithm that involves arithmetic operations and quadratic radicals. A similar fact is valid for the eigenvalue decomposition of reflections, which are Hermitian unitary matrices.

Key words: unitary matrices, symmetric matrices, Takagis decomposition, solvability by quadratic radicals

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:1, 1–3

Bibliographic databases:

UDC: 519.61
Received: 08.07.2011

Citation: Kh. D. Ikramov, “Takagis decomposition of a symmetric unitary matrix as a finite algorithm”, Zh. Vychisl. Mat. Mat. Fiz., 52:1 (2012), 4–7; Comput. Math. Math. Phys., 52:1 (2012), 1–3

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. O. Vorontsov, Kh. D. Ikramov, “Numerical algorithm for solving quadratic matrix equations of a certain class”, Comput. Math. Math. Phys., 54:11 (2014), 1643–1646  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. Marcellan F., Shayanfar N., “OPUC, CMV Matrices and Perturbations of Measures Supported on the Unit Circle”, Linear Alg. Appl., 485 (2015), 305–344  crossref  mathscinet  zmath  isi  elib  scopus
  •      Computational Mathematics and Mathematical Physics
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