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Fundam. Prikl. Mat., 2003, Volume 9, Issue 1, Pages 83–101 (Mi fpm715)  

This article is cited in 6 scientific papers (total in 6 papers)

General algebra and linear transformations preserving matrix invariants

A. È. Guterman, A. V. Mikhalev

M. V. Lomonosov Moscow State University

Abstract: The interrelations between the theory of linear transformations preserving matrix invariants and different branches of mathematics are surveyed here. The preferences are given for those methods and motivations to study these transformations that arise from general algebra.

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English version:
Journal of Mathematical Sciences (New York), 2005, 128:6, 3384–3395

Bibliographic databases:

UDC: 512.643

Citation: A. È. Guterman, A. V. Mikhalev, “General algebra and linear transformations preserving matrix invariants”, Fundam. Prikl. Mat., 9:1 (2003), 83–101; J. Math. Sci., 128:6 (2005), 3384–3395

Citation in format AMSBIB
\Bibitem{GutMik03}
\by A.~\`E.~Guterman, A.~V.~Mikhalev
\paper General algebra and linear transformations preserving matrix invariants
\jour Fundam. Prikl. Mat.
\yr 2003
\vol 9
\issue 1
\pages 83--101
\mathnet{http://mi.mathnet.ru/fpm715}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2072621}
\zmath{https://zbmath.org/?q=an:1073.15004}
\transl
\jour J. Math. Sci.
\yr 2005
\vol 128
\issue 6
\pages 3384--3395
\crossref{https://doi.org/10.1007/s10958-005-0277-x}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-22644447687}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Chebotar M.A., Fong Yuen, Lee Pjek-Hwee, “On maps preserving zeros of the polynomial $xy-yx$”, Linear Algebra Appl., 408 (2005), 230–243  crossref  mathscinet  zmath  isi  elib
    2. I. I. Bogdanov, A. È. Guterman, “Monotone matrix transformations defined by the group inverse and simultaneous diagonalizability”, Sb. Math., 198:1 (2007), 1–16  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Orel M., Kuzma B., “Additive rank-one nonincreasing maps on Hermitian matrices over the field $\mathrm{GF}(2^2)$”, Electron. J. Linear Algebra, 18 (2009), 482–499  crossref  mathscinet  zmath  isi  elib
    4. Fosner A., Kuzma B., Kuzma T., Sze N.-S., “Maps preserving matrix pairs with zero Jordan product”, Linear & Multilinear Algebra, 59:5 (2011), 507–529  crossref  mathscinet  zmath  isi
    5. V. B. Poplavskii, “Minor rank, zeros of the determinant of a Boolean matrix, and their applications”, Discrete Math. Appl., 21:5-6 (2011), 613–644  mathnet  crossref  crossref  mathscinet  elib
    6. Buergisser P., Landsberg J.M., Manivel L., Weyman J., “AN OVERVIEW OF MATHEMATICAL ISSUES ARISING IN THE GEOMETRIC COMPLEXITY THEORY APPROACH TO VP not equal VNP”, SIAM J Comput, 40:4 (2011), 1179–1209  crossref  mathscinet  zmath  isi
  • Фундаментальная и прикладная математика
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