Minghua Lin, PhD Candidate
Department of Applied Mathematics, University of Waterloo
The notion of Loewner (partial) order for general complex matrices is introduced. A square complex matrix is accretive-dissipative if both of its real and imaginary part are positive definite. After giving the definition of arithmetic, geometric and harmonic means for accretivedissipative matrices, we study their basic properties, in particular, A-G-H mean inequality is established for two accretive-dissipative matrices in the sense of this extended Loewner order.