Further results on strongly core orthogonal matrix.

Recently, Ferreyra and Malik (Core and strongly core orthogonal matrices. Linear Multilinear Algebra. 2021;1–16. doi:) have proved that if A is strongly core orthogonal to B, then rk (A + B) = rk (A) + rk (B) and (A + B) ◯ # = A ◯ # + B ◯ # . But whether the reverse holds is an open question. In this paper, we solve the problem completely and get some new characterizations of strong core orthogonality. [ABSTRACT FROM AUTHOR]