The pseudo core inverse of a lower triangular matrix (Q2314602)

Introduced in 2010 by \textit{O. M. Baksalary} and \textit{G. Trenkler} [Linear Multilinear Algebra 58, No. 5--6, 681--697 (2010; Zbl 1202.15009)], the core inverse of a complex matrix of index one was generalized to an arbitrary *-ring case by \textit{D. S. Rakić} et al. [Linear Algebra Appl. 463, 115--133 (2014; Zbl 1297.15006)]. Later, it was extended to the pseudo core inverse of an arbitrary index in *-rings and generalized to the notion of core-EP inverse for complex matrices, to the case of *-rings (see [\textit{K. M. Prasad} and \textit{K. S. Mohana}, Linear Multilinear Algebra 62, No. 6, 792--802 (2014; Zbl 1306.15006)]). In this paper, existence criteria and formulae for the pseudo core inverse of a product are presented. The explicit expression for the pseudo core inverse of a lower triangular matrix is given.