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.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 463, 2017, pp. 94–111.
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Guterman, A., Soares, G. On the Determinantal Range of Matrix Products. J Math Sci 232, 805–815 (2018). https://doi.org/10.1007/s10958-018-3910-1
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DOI: https://doi.org/10.1007/s10958-018-3910-1