More on geometry of Krein space C-numerical range

Abstract

For n × n complex matrices A, C and H, where H is non-singular Hermitian, the Krein space C-numerical range of A induced by H is the subset of the complex plane given by Tr (CU [ * ] AU ) : U −1 = U [ * ] with U [ * ] = H −1 U * H the H-adjoint matrix of U . We revisit several results on the geometry of Krein space C-numerical range of A and in particular we obtain a criteria for the Krein space C-numerical range to be a subset of the real line.