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A CANCELLATION PROPERTY OF THE MOORE–PENROSE INVERSE OF TRIPLE PRODUCTS

Published online by Cambridge University Press:  01 February 2009

TOBIAS DAMM*
Affiliation:
Fachbereich Mathematik, TU Kaiserslautern, D-67663 Kaiserslautern, Germany (email: damm@mathematik.uni-kl.de)
HARALD K. WIMMER
Affiliation:
Mathematisches Institut, Universität Würzburg, D-97074 Würzburg, Germany (email: wimmer@mathematik.uni-wuerzburg.de)
*
For correspondence; e-mail: damm@mathematik.uni-kl.de
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Abstract

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We study the matrix equation C(BXC)B=X, where X denotes the Moore–Penrose inverse. We derive conditions for the consistency of the equation and express all its solutions using singular vectors of B and C. Applications to compliance matrices in molecular dynamics, to mixed reverse-order laws of generalized inverses and to weighted Moore–Penrose inverses are given.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2009

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