Email this article On the Determinantal Range of Matrix Products
- Authors: Guterman A.1,2, Soares G.3
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Affiliations:
- Lomonosov Moscow State University
- Moscow Institute of Physics and Technology
- Mathematics Center CMAT, Pole CMAT-UTAD, Universidade de Trás-os-Montes e Alto Douro, UTAD, Escola das Ciências e Tecnologia
- Issue: Vol 232, No 6 (2018)
- Pages: 805-815
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241446
- DOI: https://doi.org/10.1007/s10958-018-3910-1
- ID: 241446
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Abstract
Let matrices A,C ∈ Mn have eigenvalues α1, . . ., αn and γ1, . . . , γn, respectively. The set of complex numbers DC(A) = {det(A−UCU*) : U ∈ Mn, U*U = In} is called the C-determinantal range of A. The paper studies various conditions under which the relation DC(R S) = DC(S R) holds for some matrices R and S.
About the authors
A. Guterman
Lomonosov Moscow State University; Moscow Institute of Physics and Technology
Author for correspondence.
Email: guterman@list.ru
Russian Federation, Moscow; Dolgoprudny
G. Soares
Mathematics Center CMAT, Pole CMAT-UTAD, Universidade de Trás-os-Montes e Alto Douro, UTAD, Escola das Ciências e Tecnologia
Email: guterman@list.ru
Portugal, Quinta dos Prados, Vila Real, 5000-801
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