Range invariance of certain matrix products
Jerzy K. Baksalary, Radosław Kala · Linear and Multilinear Algebra · 1983
A necessarv and sufficient condition is established for the product AB C to have its range.A (AB C), invariant with respect to the choice of a generalized inverse B .This result is then used to derive criteria for the invariance of the subspaces A(AB ).A(B C)A(B) and A(BB C) and also to deduce that the simultaneous invariance of the range of AB− C and the range of its conjugate transpose entails the invariance of the product AB−C itself.