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The pseudo core inverse of a lower triangular matrix. (English) Zbl 1425.15002

Introduced in 2010 by O. M. Baksalary and 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 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 [K. M. Prasad and 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.

MSC:

15A09 Theory of matrix inversion and generalized inverses
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
16S50 Endomorphism rings; matrix rings
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