Cyclotomic matrices over real quadratic integer rings

Gary Greaves

doi:10.1016/j.laa.2012.06.003

Cyclotomic matrices over real quadratic integer rings

Gary Greaves

INF - Computer and Mathematical Sciences

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

4 Citations (Scopus)

Abstract

We classify all cyclotomic matrices over real quadratic integer rings and we show that this classification is the same as classifying cyclotomic matrices over the compositum all real quadratic integer rings, R. Moreover, we enumerate a related class of symmetric R-matrices; those R-matrices whose eigenvalues are contained inside the interval [-2, 2] but whose characteristic polynomials are not in Z[x].

Original language	English
Pages (from-to)	2252-2261
Number of pages	10
Journal	Linear Algebra and Its Applications
Volume	437
Issue number	9
DOIs	https://doi.org/10.1016/j.laa.2012.06.003
Publication status	Published - 2012 Nov 1

Keywords

Cyclotomic matrices
Real quadratic integers

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.2012.06.003

Cite this

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title = "Cyclotomic matrices over real quadratic integer rings",

abstract = "We classify all cyclotomic matrices over real quadratic integer rings and we show that this classification is the same as classifying cyclotomic matrices over the compositum all real quadratic integer rings, R. Moreover, we enumerate a related class of symmetric R-matrices; those R-matrices whose eigenvalues are contained inside the interval [-2, 2] but whose characteristic polynomials are not in Z[x].",

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AB - We classify all cyclotomic matrices over real quadratic integer rings and we show that this classification is the same as classifying cyclotomic matrices over the compositum all real quadratic integer rings, R. Moreover, we enumerate a related class of symmetric R-matrices; those R-matrices whose eigenvalues are contained inside the interval [-2, 2] but whose characteristic polynomials are not in Z[x].

KW - Cyclotomic matrices

KW - Real quadratic integers

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M3 - Article

AN - SCOPUS:84864755324

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SP - 2252

EP - 2261

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 9

ER -

Cyclotomic matrices over real quadratic integer rings

Abstract

Keywords

ASJC Scopus subject areas

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