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Verifying unitary congruence of coninvolutions, skew-coninvolutions, and connilpotent matrices of index two

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It is shown that n× n solutions A and B of the matrix equation

$$ X\overline X = \delta I, $$

where δ is one and the same for both matrices, are unitarily congruent if and only if

$$ {\text{tr}}{\left( {A*A} \right)^k} = {\text{tr}}{\left( {B*B} \right)^k},\,\,\,k = 1,2, \ldots, n. $$

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    Kh. D. Ikramov

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  1. Kh. D. Ikramov
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Correspondence to Kh. D. Ikramov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 367, 2009, pp. 27–32.

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Ikramov, K.D. Verifying unitary congruence of coninvolutions, skew-coninvolutions, and connilpotent matrices of index two. J Math Sci 165, 511–514 (2010). https://doi.org/10.1007/s10958-010-9820-5

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  • DOI: https://doi.org/10.1007/s10958-010-9820-5

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