A Relation Between the Moore-Penrose and Commuting Reciprocal Inverses

If a singular square matrix has both a commuting reciprocal and Moore-Penrose inverse, it is proved that either of these may be factorized in terms of the other. Examples related to singular boundary value problems are given.

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Bibliographic Details
Published in:SIAM journal on applied mathematics 1973-01, Vol.24 (1), p.44-49
Main Authors: Lovass-Nagy, V., Powers, D. L.
Format: Article
Language:English
Subjects:
Boundary value problems
Commuting
Eigenvalues
Linear algebra
Mathematical relations
Mathematics
Matrices
Partial differential equations
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Description
Summary:If a singular square matrix has both a commuting reciprocal and Moore-Penrose inverse, it is proved that either of these may be factorized in terms of the other. Examples related to singular boundary value problems are given.
ISSN:0036-1399
1095-712X
DOI:10.1137/0124006