ON THE DETERMINANTAL RANGE OF MATRIX PRODUCTS

摘要

Let matrices A , C ∈ M ~( n )have eigenvalues α ~(1), . . ., α ~( n )and γ ~(1), . . . , γ ~( n ), respectively. The set of complex numbers D ~( C )( A ) = {det( A − UCU *) : U ∈ M ~( n ), U * U = I ~( n )} is called the C -determinantal range of A . The paper studies various conditions under which the relation D ~( C )( R S ) = D ~( C )( S R ) holds for some matrices R and S .