Perturbations of determinants of matrices

Michael Gil'

doi:10.1016/j.laa.2019.12.044

Perturbations of determinants of matrices

Michael Gil'

Department of Mathematics

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

4 Scopus citations

Abstract

Let A,A˜ be n×n-matrices and {d_k} be an arbitrary orthonormal basis in Cⁿ. It is proved that the determinants satisfy the inequality [Formula presented] where ‖.‖ is the Euclidean norm and q=max_k⁡‖(A−A˜)d_k‖.

Original language	English
Pages (from-to)	235-242
Number of pages	8
Journal	Linear Algebra and Its Applications
Volume	590
DOIs	https://doi.org/10.1016/j.laa.2019.12.044
State	Published - 1 Apr 2020

Keywords

Bounds for determinants
Perturbations of determinants

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.2019.12.044

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title = "Perturbations of determinants of matrices",

abstract = "Let A,A˜ be n×n-matrices and {dk} be an arbitrary orthonormal basis in Cn. It is proved that the determinants satisfy the inequality [Formula presented] where ‖.‖ is the Euclidean norm and q=maxk⁡‖(A−A˜)dk‖.",

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N2 - Let A,A˜ be n×n-matrices and {dk} be an arbitrary orthonormal basis in Cn. It is proved that the determinants satisfy the inequality [Formula presented] where ‖.‖ is the Euclidean norm and q=maxk⁡‖(A−A˜)dk‖.

AB - Let A,A˜ be n×n-matrices and {dk} be an arbitrary orthonormal basis in Cn. It is proved that the determinants satisfy the inequality [Formula presented] where ‖.‖ is the Euclidean norm and q=maxk⁡‖(A−A˜)dk‖.

KW - Bounds for determinants

KW - Perturbations of determinants

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DO - 10.1016/j.laa.2019.12.044

M3 - Article

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VL - 590

SP - 235

EP - 242

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Perturbations of determinants of matrices

Abstract

Keywords

ASJC Scopus subject areas

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