Secondary transpose of matrix and generalized inverses

Abstract

In this paper, several existing results related to secondary transpose are critically reviewed and a result analogous to spectral decomposition theorem is obtained for a real secondary symmetric matrix. Noting that Moore–Penrose inverse with reference to secondary transpose involution, namely [Formula: see text]-g inverse, need not always exist, we explore a few necessary sufficient conditions for the existence of such Moore–Penrose inverse. Further, we provide expressions and determinantal formula to compute the same.

Secondary range symmetric matrices

“…In Ref. 10 , a necessary and sufficient conditions of existence of s-g invese is given. In the same article, a few characterizations and a determinantal formula for s-g inverse also has been discussed.…”