摘要
An inverse G of a given matrix A satisfying the condition GAG=G is known as a {2}-inverse of A. This paper makes the {2}-inverse the starting point for studying the Lowner partial ordering of real nonnegative matrices. Simple basic properties of the {2}-inverses yield various extensions for the reverse ordering property, AB if and only if B-1A-1, of the positive definite matrices.
An inverse G of a given matrix A satisfying the condition GAG=G is known as a {2}-inverse of A. This paper makes the {2}-inverse the starting point for studying the Lowner partial ordering of real nonnegative matrices. Simple basic properties of the {2}-inverses yield various extensions for the reverse ordering property, AB if and only if B-1A-1, of the positive definite matrices.
