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

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• 作者：M.A. Rodrí ; guez-Andrade^a ; ^b ; ^{marco@esfm.ipn.mx" class="auth_mail" title="E-mail the corresponding author} ; G. Aragó ; n-Gonzá ; lez^c ; ^{gag@correo.azc.uam.mx" class="auth_mail" title="E-mail the corresponding author} ; J.L. Aragó ; n^d ; ^{aragon@fata.unam.mx" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15B10 ; 15A23 ; 15A66
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：496
• 期：Complete
• 页码：101-113
• 全文大小：322 K

文摘

A method for generating all rational generalized matrices on indefinite real inner product spaces isomorphic to R^p,q$R^{p,q}$ 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$\mathcal{B}$-orthogonal matrices in an indefinite inner product space (X,B)$(\mathcal{X},\mathcal{B})$ are products of simple matrices with rational entries.