Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 3 , pp. 458-464

GENERALIZED INVERSES OF A SUM OF MATRICES

By

RADOSLAW KALA and KRZYSZTOF KLACZY\'{N}SKI, Agricultural University of Pozna\'{n}, Poland

SUMMARY. The representation of various generalized inverses of the sum of two (i) rectangular matrices, of the form $A + BDC^*$, and (ii) nonnegative definite matrices, of the form $A + BDB^*$, are established. The formulae obtained do not require the assumptions that the range of $A$ contains (i) the range of $BDC^*$ or (ii) the range of $BDB^*$.

AMS (1980) subject classification. Primary 15A09, secondary 62J05.

Key words and phrases. Generalized inverse of sum of rectangular matrices, genealized inverse of sum of nonnegative definite matrices, Hermitian matrices, general Gauss-Markov model, best linear unbiased estimation.

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