Geodesic
On the determinantal range of matrix products
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 94-111

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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 $S$. 
@article{ZNSL_2017_463_a7,
     author = {A. Guterman and G. Soares},
     title = {On the determinantal range of  matrix products},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {94--111},
     publisher = {mathdoc},
     volume = {463},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a7/}
}
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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/