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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Inverses of infinite sign regular matrices


Authors: C. de Boor, S. Friedland and A. Pinkus
Journal: Trans. Amer. Math. Soc. 274 (1982), 59-68
MSC: Primary 47B37; Secondary 15A09
MathSciNet review: 670918
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Abstract: Let $ A$ be an infinite sign regular (sr) matrix which can be viewed as a bounded linear operator from $ {l_\infty }$ to itself. It is proved here that if the range of $ A$ contains the sequence $ ( \ldots ,1, - 1,1, - 1, \ldots )$, then $ A$ is onto. If $ {A^{ - 1}}$ exists, then $ D{A^{ - 1}}D$ is also sr, where $ D$ is the diagonal matrix with diagonal entries alternately $ 1$ and $ - 1$. In case $ A$ is totally positive (tp), then $ D{A^{ - 1}}D$ is also tp under additional assumptions on $ A$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0670918-7
PII: S 0002-9947(1982)0670918-7
Keywords: Bi-infinite, infinite, matrix, total positivity, sign regularity, inverse
Article copyright: © Copyright 1982 American Mathematical Society