On a theorem of Rao on g-inverses of matrices

Abstract

Consider matrices Ai(m × ni)i =1(1)k and let Λ(m × m) be a p.d. matix. Rao(1967) shows that if Σ R(Ai)=m, Λ-1=Σ Ai(A•iΛ Ai)-A•i ⇔ A•i Λ Aj =0 for each i, j, i ≠ j. The present note gives an interesting generalisation of this theorem of Rao