Banach Journal of Mathematical Analysis

A 1-norm bound for inverses of triangular matrices with monotone entries

Kenneth S. Berenhaut , Richard T. Guy , and Nathaniel G. Vish

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Abstract

This paper provides some new bounds for $1-$norms of positive triangular matrices with monotonic column entries. The main theorem refines a recent inequality of Vecchio and Mallik in the case of constant diagonal. The results are shown to be in a sense best possible under the given constraints. En route some partial order inequalities are obtained.

Article information

Source
Banach J. Math. Anal., Volume 2, Number 1 (2008), 113 -122 .

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240336280

Digital Object Identifier
doi:10.15352/bjma/1240336280

Mathematical Reviews number (MathSciNet)
MR2417528

Zentralblatt MATH identifier
1147.15018

Subjects
Primary: 15A09: Matrix inversion, generalized inverses
Secondary: 39A10: Difference equations, additive 15A57 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]

Keywords
inverse matrix monotone entries triangular matrix partial order recurrence relation

Citation

Berenhaut , Kenneth S.; Guy , Richard T.; Vish , Nathaniel G. A 1-norm bound for inverses of triangular matrices with monotone entries. Banach J. Math. Anal. 2 (2008), no. 1, 113 --122. doi:10.15352/bjma/1240336280. https://projecteuclid.org/euclid.bjma/1240336280


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References

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