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The J-Householder matrices

Let J=0I-I0∈M2n(C). Let 0≠u∈C2n be given. A J-Householder matrix corresponding to u is Hu≡I-uuTJ. We show that every symplectic matrix is a product of J-Householder matrices. We present properties of J-Householder matrices, and we also present the possible Jordan Canonical Forms of products of two J...

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Bibliographic Details
Published in:Linear algebra and its applications 2012-03, Vol.436 (5), p.1189-1194
Main Authors: de la Rosa, Kennett L., Merino, Dennis I., Paras, Agnes T.
Format: Article
Language:English
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Summary:Let J=0I-I0∈M2n(C). Let 0≠u∈C2n be given. A J-Householder matrix corresponding to u is Hu≡I-uuTJ. We show that every symplectic matrix is a product of J-Householder matrices. We present properties of J-Householder matrices, and we also present the possible Jordan Canonical Forms of products of two J-Householder matrices.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2011.08.002