Generalized Inverses of a Sum of Matrices

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*...

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Bibliographic Details
Published in:Sankhya. Series A 1994-10, Vol.56 (3), p.458-464
Main Authors: Kala, Radoslaw, Klaczyński, Krzysztof
Format: Article
Language:English
Subjects:
Linear models
Mathematics
Matrices
Scalars
Online Access:Get full text
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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*.
ISSN:0581-572X