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Matematicheskie Zametki, 2010, Volume 87, Issue 6, Pages 840–847
DOI: https://doi.org/10.4213/mzm8532 (Mi mzm8532) 		 
This article is cited in 9 scientific papers (total in 9 papers)

On Complex Matrices that Are Unitarily Similar to Real Matrices

Kh. D. Ikramov

M. V. Lomonosov Moscow State University
Full-text PDF (437 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm8532
Abstract: There are well-known conditions ensuring that a complex $n\times n$ matrix $A$ can be converted by a similarity transformation into a real matrix. Is it possible to realize this conversion via unitary similarity rather than a general one? The following answer to this question is given in this paper: A matrix $A\in M_n(\mathbb C)$ can be made real by a unitary similarity transformation if and only if $A$ and $\overline A$ are unitarily similar and the matrix $P$ transforming $A$ into $\overline A$ can be chosen unitary and symmetric at the same time. Effective ways for verifying this criterion are discussed.
Keywords: complex matrix, unitary similarity transformation, irreducible matrix, block quaternion, Jordan block, Specht's criterion.
Received: 03.08.2009
Revised: 01.12.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 6, Pages 821–827
DOI: https://doi.org/10.1134/S0001434610050214
Bibliographic databases:
Document Type: Article
UDC: 512.643
Language: Russian
Citation: Kh. D. Ikramov, “On Complex Matrices that Are Unitarily Similar to Real Matrices”, Mat. Zametki, 87:6 (2010), 840–847; Math. Notes, 87:6 (2010), 821–827
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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