On a theorem of Rao on g-inverses of matrices

Bhimasankaram, P. ; Mitra, Sujit Kumar (1969) On a theorem of Rao on g-inverses of matrices Sankhya - Series A, 31 (3). pp. 365-368. ISSN 0581-572X

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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(AiΛ Ai)-Ai ⇔ Ai Λ Aj =0 for each i, j, i ≠ j. The present note gives an interesting generalisation of this theorem of Rao.

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