This article is cited in 1 paper

The polarization theorem and polynomial identities for matrix functions

G. P. Egorychev

Siberian Federal University, 26, Kirenskii st., Krasnoyarsk, 660074

Abstract: In this article the simple combinatorial proof of the known polarization theorem (about the restoration of a polyadditive symmetric function over its values on a diagonal) is given. Known and new applications of this theorem for the reception of polynomial identities (the calculation) of several matrix functions is given, including a case of noncommutative variables and (first) the determinant of a space matrix are resulted.

Keywords: polarization theorem, determinants, permanents, polynomial identities, noncommutative variables.

UDC: 512.64+512.55

MSC: 15+16

DOI: 10.26516/1997-7670.2017.21.77

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