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

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

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 ge...

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Veröffentlicht in:Journal of the Australian Mathematical Society (2001) 2009-02, Vol.86 (1), p.33-44
Hauptverfasser: DAMM, TOBIAS, WIMMER, HARALD K.
Format: Artikel
Sprache:eng
Schlagworte:
15A90
compliance matrix
Mathematical analysis
matrix equations
Molecular dynamics
Moore–Penrose generalized inverse
primary 15A09
reverse-order property
secondary 15A24
Wedderburn–Guttman theorem
weighted generalized inverse
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Zusammenfassung: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.
ISSN:1446-7887
1446-8107
DOI:10.1017/S144678870800044X