The Generalized Inverse Inequalities for Symmetric Nonnegative Definite Matrices

摘要

Let be symmetric positive definite matrix, symmetric nonnegative definite matrix. If the difference of and is positive definite, then the difference of and is also positive definite. If, are all symmetric nonnegative definite matrices, Milliken and Akdeniz (1977) proved that they also have this relationship if only the ranks of the two matrices are same. That is the difference of and is symmetric nonnegative definite, where is Penrose-Moore inverse matrix of . Wang (2010) improved this inequality and extended by his result Belmegaȁ9;s (2009) a theorem. In this paper, we give some inequalities of the sum and the product for symmetric nonnegative definite matrix. They all extend Milliken and Akdenizȁ9;s (1977) and Wangȁ9;s (2010) results.