Moore-Penrose inverse of an invertible infinite matrix

In this article we show that, contrary to finite matrices (with real or complex entries) an invertible infinite matrix V could have a Moore-Penrose inverse that is not a classical inverse of V. This also answers a recent open problem on infinite matrices.

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 54; no. 1; pp. 71 - 77
Main Author Sivakumar, K. C.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.01.2006
Subjects
AMS Subject Classification: Primary 15A09
Infinite matrices
Moore-Penrose inverse
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Summary:In this article we show that, contrary to finite matrices (with real or complex entries) an invertible infinite matrix V could have a Moore-Penrose inverse that is not a classical inverse of V. This also answers a recent open problem on infinite matrices.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081080500054265