Interval matrices: Regularity generates singularity

Jiri Rohn; Sergey P. Shary

doi:10.1016/j.laa.2017.11.020

Interval matrices: Regularity generates singularity

Jiri Rohn, Sergey P. Shary

Mathematical Modeling Section

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

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Abstract

It is proved that regularity of an interval matrix implies singularity of four related interval matrices. The result is used to prove that for each nonsingular point matrix A, either A or A⁻¹ can be brought to a singular matrix by perturbing only the diagonal entries by an amount of at most 1 each. As a consequence, the notion of a diagonally singularizable matrix is introduced.

Original language	English
Pages (from-to)	149-159
Number of pages	11
Journal	Linear Algebra and Its Applications
Volume	540
DOIs	https://doi.org/10.1016/j.laa.2017.11.020
Publication status	Published - 1 Mar 2018

Keywords

Absolute value equation
Diagonally singularizable matrix
Interval matrix
P-matrix
Regularity
Singularity

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10.1016/j.laa.2017.11.020

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title = "Interval matrices: Regularity generates singularity",

abstract = "It is proved that regularity of an interval matrix implies singularity of four related interval matrices. The result is used to prove that for each nonsingular point matrix A, either A or A−1 can be brought to a singular matrix by perturbing only the diagonal entries by an amount of at most 1 each. As a consequence, the notion of a diagonally singularizable matrix is introduced.",

keywords = "Absolute value equation, Diagonally singularizable matrix, Interval matrix, P-matrix, Regularity, Singularity",

author = "Jiri Rohn and Shary, {Sergey P.}",

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AU - Shary, Sergey P.

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N2 - It is proved that regularity of an interval matrix implies singularity of four related interval matrices. The result is used to prove that for each nonsingular point matrix A, either A or A−1 can be brought to a singular matrix by perturbing only the diagonal entries by an amount of at most 1 each. As a consequence, the notion of a diagonally singularizable matrix is introduced.

AB - It is proved that regularity of an interval matrix implies singularity of four related interval matrices. The result is used to prove that for each nonsingular point matrix A, either A or A−1 can be brought to a singular matrix by perturbing only the diagonal entries by an amount of at most 1 each. As a consequence, the notion of a diagonally singularizable matrix is introduced.

KW - Absolute value equation

KW - Diagonally singularizable matrix

KW - Interval matrix

KW - P-matrix

KW - Regularity

KW - Singularity

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SP - 149

EP - 159

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

Interval matrices: Regularity generates singularity

Abstract

Keywords

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