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Zh. Vychisl. Mat. Mat. Fiz., 2011, Volume 51, Number 4, Pages 547–554 (Mi zvmmf9223)  

On complex matrices with simple spectrum that are unitarily similar to real matrices

Kh. D. Ikramov

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

Abstract: Suppose that one should verify whether a given complex $n\times n$ matrix can be converted into a real matrix by a unitary similarity transformation. Sufficient conditions for this property to hold were found in an earlier publication of this author. These conditions are relaxed in the following way: as before, the spectrum is required to be simple, but pairs of complex conjugate eigenvalues $\lambda$, $\bar\lambda$, are now allowed. However, the eigenvectors corresponding to such eigenvalues must not be orthogonal.

Key words: unitary similarity transformation, unitary congruence transformation, Takagi's theorem, Specht's criterion, coneigenvalues, Schur form, semilinear matrix equation.

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English version:
Computational Mathematics and Mathematical Physics, 2011, 51:4, 505–512

Bibliographic databases:

UDC: 519.61
Received: 14.12.2009

Citation: Kh. D. Ikramov, “On complex matrices with simple spectrum that are unitarily similar to real matrices”, Zh. Vychisl. Mat. Mat. Fiz., 51:4 (2011), 547–554; Comput. Math. Math. Phys., 51:4 (2011), 505–512

Citation in format AMSBIB
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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