Further characterizations and representations of the Bott-Duffin core inverse

Abstract

The purpose of this paper is to discuss some new characterizations and representations of the Bott-Duffin core inverse. We characterize the Bott-Duffin core inverse by using the orthogonal projectors, the matrix equation, the Bott-Duffin group inverse and the solution of the block-rank equation. Some representations of Bott-Duffin core inverse are presented by using the full-rank decomposition. Finally, we provide the least-squares solution of the constraint system of linear equations.