Conditions for the generalized numerical range to be real
Let C and A be given \(n\times n\) matrices. The classical numerical range \(W(CU^*AU)\) is contained in the real axis for all unitary U iff at least one of C and A is scalar and their product is Hermitian. The authors also investigate two generalized numerical ranges and describe the situations where these are real, or contained in a line parallel to the real axis.
scientific article; zbMATH DE number 3933240
scientific article