ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2017. Vol. 21

The Polarization Theorem and Polynomial Identities for Matrix Functions

G. P. Egorychev

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.

polarization theorem, determinants, permanents, polynomial identities, noncommutative variables

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