Geodesic
On the determinantal range of matrix products
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 94-111 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $S$. 
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A. Guterman; G. Soares. On the determinantal range of matrix products. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 94-111. http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a7/

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