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Mat. Zametki, 2012, Volume 92, Issue 6, Pages 856–863 (Mi mz9195)  

Effective Algorithms for Decomplexifying a Matrix by Unitary Similarities or Congruences

Kh. D. Ikramov

M. V. Lomonosov Moscow State University

Abstract: It is required to verify whether a given complex $n\times n$ matrix $A$ can be made real by a similarity or a congruence transformation. Algorithms for solving these two problems are proposed and justified under the additional assumption that $A$ is irreducible in the former case and $A_L=\overline AA$ is irreducible in the latter case. The irreducibility of a square complex matrix means that no unitary similarity transformation converts this matrix into a direct sum of smaller matrices. The proposed algorithms are effective in the sense that their implementation requires a finite number of arithmetic operations.

Keywords: unitary similarity, unitary congruence, irreducible matrix, polar decomposition, consimilarity

DOI: https://doi.org/10.4213/mzm9195

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English version:
Mathematical Notes, 2012, 92:6, 767–772

Bibliographic databases:

UDC: 512.643
Received: 14.07.2011

Citation: Kh. D. Ikramov, “Effective Algorithms for Decomplexifying a Matrix by Unitary Similarities or Congruences”, Mat. Zametki, 92:6 (2012), 856–863; Math. Notes, 92:6 (2012), 767–772

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