Article,

Generalized Inversion of Modified Matrices

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SIAM J. Appl. Math., 24 (3): 315--323 (May 1973)
DOI: 10.1137/0124033

Abstract

For an $m n$ complex matrix A and two columns, c and d, representations for the Moore–Penrose inverse of the matrix $A + cd^ * $ are given for all possible cases. Moreover, each representation involves only A, $A^$, c, d, and their conjugate transposes.

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