Diagonal entries of inverses of diagonally dominant matrices

C. R. Johnson; C. Marijuán; M. Pisonero; I. M. Spitkovsky

doi:10.1016/j.laa.2024.04.005

Diagonal entries of inverses of diagonally dominant matrices

C. R. Johnson, C. Marijuán, M. Pisonero, I. M. Spitkovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider invertible, row diagonally dominant real matrices and give inequalities on their minors and diagonal entries of their inverses. A very special case is that all diagonal entries of an inverse, of a row stochastic, row diagonally dominant and invertible matrix, are at least 1, with strict inequality at least when the dominance is strict. This was conjectured in international trade theory in economics and motivated the present work (though much more is proven). Some of the results generalize previously known facts for M-matrices.

Original language	English (US)
Pages (from-to)	84-90
Number of pages	7
Journal	Linear Algebra and Its Applications
Volume	692
DOIs	https://doi.org/10.1016/j.laa.2024.04.005
State	Published - Jul 1 2024

Keywords

Diagonal dominance of the column entries
Diagonal entries of the inverse
Diagonally dominant matrices
Inequalities for minors
Stochastic matrices

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2024.04.005

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abstract = "We consider invertible, row diagonally dominant real matrices and give inequalities on their minors and diagonal entries of their inverses. A very special case is that all diagonal entries of an inverse, of a row stochastic, row diagonally dominant and invertible matrix, are at least 1, with strict inequality at least when the dominance is strict. This was conjectured in international trade theory in economics and motivated the present work (though much more is proven). Some of the results generalize previously known facts for M-matrices.",

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AU - Johnson, C. R.

AU - Marijuán, C.

AU - Pisonero, M.

AU - Spitkovsky, I. M.

PY - 2024/7/1

Y1 - 2024/7/1

N2 - We consider invertible, row diagonally dominant real matrices and give inequalities on their minors and diagonal entries of their inverses. A very special case is that all diagonal entries of an inverse, of a row stochastic, row diagonally dominant and invertible matrix, are at least 1, with strict inequality at least when the dominance is strict. This was conjectured in international trade theory in economics and motivated the present work (though much more is proven). Some of the results generalize previously known facts for M-matrices.

AB - We consider invertible, row diagonally dominant real matrices and give inequalities on their minors and diagonal entries of their inverses. A very special case is that all diagonal entries of an inverse, of a row stochastic, row diagonally dominant and invertible matrix, are at least 1, with strict inequality at least when the dominance is strict. This was conjectured in international trade theory in economics and motivated the present work (though much more is proven). Some of the results generalize previously known facts for M-matrices.

KW - Diagonal dominance of the column entries

KW - Diagonal entries of the inverse

KW - Diagonally dominant matrices

KW - Inequalities for minors

KW - Stochastic matrices

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DO - 10.1016/j.laa.2024.04.005

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SN - 0024-3795

VL - 692

SP - 84

EP - 90

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Diagonal entries of inverses of diagonally dominant matrices

Abstract

Keywords

ASJC Scopus subject areas

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