Strong majorization for Hermitian matrices Original Research Article

We introduce and study an additive relation and a multiplicative relation for hermitian matrices. The relation G < a F means that F is the real part of some matrix similar to G; the relation G < m F expresses the property that the positive definite matrix F is the modulus of some matrix similar to the positive definite matrix G. There is a close connection with the (additive and multiplicative) majorization relations for the corresponding spectra.