DMS Linear Algebra/Algebra Seminar

Speaker:  Xiaoji Liu

Title: Partial order of matrices and generalized inverse

Abstract: Many researchers in the field have paid much attention to minus-type partial orders, and have scored fruitful findings. Findings with respect to non-minus-type partial orders, though comparatively few, have greatly enriched the matrix partial order theory. We derive some characterizations of the C-N partial ordering, create a new partial ordering (the G-Drazin partial ordering) , and  by using the L¨owner partial order and the core partial order, we introduce a new partial order (the CL partial ordering) on the set of core matrices. We will present some results relating the Sharp ordering (a ≤♯ b) and investigate the properties of one-sided cyclic ideals generated by the group or Moore--Penrose invertible element in rings.  In the last section, we consider the following matrix inequality:  AXA<A  in the star, sharp and core partial orders, respectively.