Secondary transpose of matrix and generalized inverses

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.