The generation of all rational orthogonal matrices in Rp,q

M. A. Rodríguez-Andrade; G. Aragón-González; J. L. Aragón

doi:10.1016/j.laa.2015.12.031

The generation of all rational orthogonal matrices in R^p,q

M. A. Rodríguez-Andrade, G. Aragón-González, J. L. Aragón

Escuela Superior de Física y Matemáticas (ESFM)

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

1 Scopus citations

Abstract

A method for generating all rational generalized matrices on indefinite real inner product spaces isomorphic to ^Rp,q is presented. The proposed method is based on the proof of a weak version of the Cartan-Dieudonné theorem, handled using Clifford algebras. It is shown that all rational B-orthogonal matrices in an indefinite inner product space (X,B) are products of simple matrices with rational entries.

Original language	English
Pages (from-to)	101-113
Number of pages	13
Journal	Linear Algebra and Its Applications
Volume	496
DOIs	https://doi.org/10.1016/j.laa.2015.12.031
State	Published - 1 May 2016

Keywords

Cartan-Dieudonné
Clifford algebras
Householder transformations
Orthogonal matrices

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10.1016/j.laa.2015.12.031

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AB - A method for generating all rational generalized matrices on indefinite real inner product spaces isomorphic to Rp,q is presented. The proposed method is based on the proof of a weak version of the Cartan-Dieudonné theorem, handled using Clifford algebras. It is shown that all rational B-orthogonal matrices in an indefinite inner product space (X,B) are products of simple matrices with rational entries.

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KW - Clifford algebras

KW - Householder transformations

KW - Orthogonal matrices

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

The generation of all rational orthogonal matrices in R^p,q

Abstract

Keywords

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