  The concept of Loewner (partial) order for general complex matrices is
introduced. After giving the definition of arithmetic, geometric, and harmonic
mean for accretive-dissipative matrices, we study their basic properties. An
AM-GM-HM inequality is established for two accretive-dissipative matrices in
the sense of this extended Loewner order. We also compare the harmonic mean and
parallel sum of two accretive-dissipative matrices, revealing an interesting
relation between them. A number of examples are included.
