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The Bulletin of Irkutsk State University. Series Mathematics, 2012, Volume 5, Issue 4, Pages 16–20 (Mi iigum81)  

This article is cited in 2 scientific papers (total in 2 papers)

New polynomial identities for determinants over commutative rings

G. P. Egorychev

Siberian Federal University, 26, Kirenskogo St., Krasnoyarsk, 660074

Abstract: Let $K$ be a commutative ring with division by integers. Here we give a new family of polynomial identities (calculation formulas) for determinants over the ring $K$ using the well-known polarization theorem, which allows us a new criterian for linear independence of $n$ vectors in $\mathbb{C}^{n}$.

Keywords: determinants; commutative rings; polynomial identities.

Full text: PDF file (248 kB)
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UDC: 512.64+512.55

Citation: G. P. Egorychev, “New polynomial identities for determinants over commutative rings”, The Bulletin of Irkutsk State University. Series Mathematics, 5:4 (2012), 16–20

Citation in format AMSBIB
\Bibitem{Ego12}
\by G.~P.~Egorychev
\paper New polynomial identities for determinants over commutative rings
\jour The Bulletin of Irkutsk State University. Series Mathematics
\yr 2012
\vol 5
\issue 4
\pages 16--20
\mathnet{http://mi.mathnet.ru/iigum81}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. P. Egorychev, “Teorema polyarizatsii i polinomialnye tozhdestva dlya matrichnykh funktsii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 21 (2017), 77–88  mathnet  crossref
    2. G. P. Egorychev, “Determinanty kak kombinatornye formuly summirovaniya nad algebroi s edinstvennoi $n$-arnoi operatsiei”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 26 (2018), 121–127  mathnet  crossref
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