Geodesic
The polarization theorem and polynomial identities for matrix functions
The Bulletin of Irkutsk State University. Series Mathematics, Tome 21 (2017), pp. 77-88

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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
Mots-clés : noncommutative variables. 
@article{IIGUM_2017_21_a5,
     author = {G. P. Egorychev},
     title = {The polarization theorem and polynomial identities for matrix functions},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {77--88},
     publisher = {mathdoc},
     volume = {21},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2017_21_a5/}
}
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G. P. Egorychev. The polarization theorem and polynomial identities for matrix functions. The Bulletin of Irkutsk State University. Series Mathematics, Tome 21 (2017), pp. 77-88. http://geodesic.mathdoc.fr/item/IIGUM_2017_21_a5/