The Equivalence of Two Partial Orders on A Convex Cone ofPositive

@inproceedings{Mathias2001TheEO,
  title={The Equivalence of Two Partial Orders on A Convex Cone ofPositive},
  author={Roy Mathias},
  year={2001}
}
The Loewner partial order is deened on the space of Hermitian matrices by A B if A ? B is positive semideenite. Given a strictly increasing function f :(a; b) ! R we deene the partial order f on the set of Hermitian matrices with spectrum contained in (a; b) by A f B if f(A) f(B): We say that the partial orders and f are equivalent on a set S of Hermitian matrices if A B if and only if A f B for all A; B 2 S: It is clear that if the cone C is commutative, i.e., AB = BA for all A; B 2 C, then… CONTINUE READING