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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 463, Pages 94–111 (Mi znsl6509)  
This article is cited in 1 scientific paper (total in 1 paper)

On the determinantal range of matrix products

A. Gutermana, G. Soaresb

a Lomonosov Moscow State University, Russia
b Universidade de Trás-os-Montes e Alto Douro, Portugal
Full-text PDF (244 kB) Citations (1)
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Abstract: Let matrices $A,C\in M_n$ have eigenvalues $\alpha_1,\dots,\alpha_n$ and $\gamma_1,\dots,\gamma_n$, respectively. The set $D_C(A)=\{\det(A-UCU^*)\colon U\in M_n,\ U^*U=I_n\}$ of complex numbers is called the $C$-determinantal range of $A$. The paper studies various conditions under which the relation $D_C(RS)=D_C(SR)$ holds for some matrices $R$ and $S$.
Key words and phrases: $C-$determinantal range, numerical range, matrix products.
Funding agency Grant number
Russian Science Foundation 17-11-01124
Fundação para a Ciência e a Tecnologia UID/MAT/00013/2013
Received: 01.11.2017
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 232, Issue 6, Pages 805–815
DOI: https://doi.org/10.1007/s10958-018-3910-1
Bibliographic databases:
Document Type: Article
UDC: 512.643
Language: Russian
Citation: A. Guterman, G. Soares, “On the determinantal range of matrix products”, Computational methods and algorithms. Part XXX, Zap. Nauchn. Sem. POMI, 463, POMI, St. Petersburg, 2017, 94–111; J. Math. Sci. (N. Y.), 232:6 (2018), 805–815
Citation in format AMSBIB
\Bibitem{GutSoa17}
\by A.~Guterman, G.~Soares
\paper On the determinantal range of matrix products
\inbook Computational methods and algorithms. Part~XXX
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 463
\pages 94--111
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6509}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 232
\issue 6
\pages 805--815
\crossref{https://doi.org/10.1007/s10958-018-3910-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048974557}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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