C-S and Strongly C-S Orthogonal Matrices

Abstract

In this paper, we present a new concept of the generalized core orthogonality (called the C-S orthogonality) for two generalized core invertible matrices A and B. A is said to be C-S orthogonal to B if ASB=0 and BAS=0, where AS is the generalized core inverse of A. The characterizations of C-S orthogonal matrices and the C-S additivity are also provided. And, the connection between the C-S orthogonality and C-S partial order has been given using their canonical form. Moreover, the concept of the strongly C-S orthogonality is defined and characterized.