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Inverses of Infinite Sign Regular Matrices.

Author: C DE Boor; S Friedland; A Pinkus; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER.
Publisher: Ft. Belvoir Defense Technical Information Center DEC 1980.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
Let A be an infinite sign regular (SR) matrix which can be viewed as a bounded linear operator from L sub infinity to itself. It is proved here that if the range of A contains the sequence (...,1,-1,1,-1, ...), then A is onto. If (inverse of A) exists then D (inverse of A) 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 (inverse of  Read more...
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Document Type: Book
All Authors / Contributors: C DE Boor; S Friedland; A Pinkus; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER.
OCLC Number: 227480477
Description: 19 p.

Abstract:

Let A be an infinite sign regular (SR) matrix which can be viewed as a bounded linear operator from L sub infinity to itself. It is proved here that if the range of A contains the sequence (...,1,-1,1,-1, ...), then A is onto. If (inverse of A) exists then D (inverse of A) 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 (inverse of A) D is also TP under additional assumptions on A. (Author).

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