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

Part of: Basic linear algebra

Published online by Cambridge University Press:  01 February 2009

TOBIAS DAMM  and
HARALD K. WIMMER
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.

Keywords

Moore–Penrose generalized inversecompliance matrixreverse-order propertyweighted generalized inverseWedderburn–Guttman theoremmatrix equations

MSC classification

Secondary: 15A09: Matrix inversion, generalized inverses
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 1 , February 2009 , pp. 33 - 44
Copyright
Copyright © Australian Mathematical Society 2009

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