Survey on Star Partial Order in Indefinite Inner Product Spaces

Ivana Stanišev

This is a short survey on the star partial order for matrices which is considered in the spaces with indefinite metric. The specific geometry of these spaces effects even on the definition of a star partial order, demanding the existence of the Moore--Penrose inverse of a certain matrix. A characterization of this partial order is also given. Some of the interesting properties are generalized and illustrated by the appropriate examples.