Weighted composite outer inverses


Mosić, D., Stanimirović, P. S., & Katsikis, V. N. (2021). Weighted composite outer inverses. Applied Mathematics and Computation, 411, 126493. Copy at http://www.tinyurl.com/yhetbok9


In order to extend and unify the definitions of W-weighted DMP, W-weighted MPD, W-weighted CMP and composite outer inverses, we present the weighted composite outer inverses. Precisely, the notions of MNOMP, MPMNO and MPMNOMP inverses are introduced as appropriate expressions involving the (M,N)-weighted (B,C)-inverse and Moore–Penrose inverse. Basic properties and a number of characterizations for the MNOMP, MPMNO or MPMNOMP inverse are discovered. Various representations and characterizations of weighted composite outer inverses are studied. General solutions for certain systems of linear equations are given in terms of weighted composite outer inverses. Numerical examples are presented on randomly generated matrices of various orders.