On the diagonalizability of a matrix by a symplectic equivalence, similarity or congruence transformation

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• 作者：Ralph John de la Cruz^a ; ^{rjdelacruz@math.upd.edu.ph" class="auth_mail" title="E-mail the corresponding author} ; Heike Faß ; bender^b ; ^{h.fassbender@tu-braunschweig.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A21 ; 15A23
• 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：288-306
• 全文大小：402 K

文摘

A symplectic matrix S∈C^2n×2n$S\in {\mathbb{C}}^{2n\times 2n}$ satisfies S=J⁻¹S^TJ$S=J^{-1}{S}^{T}J$ for $J=\left[\genfrac{}{}{0ex}{}{0}{-I_n}\genfrac{}{}{0ex}{}{I_n}{0}\right]\in {\mathbb{R}}^{2n\times 2n}$. We will consider symplectic equivalence, similarity and congruence transformations and answer the question under which conditions a 3d94da57cb136e1290ced992a34cf0" title="Click to view the MathML source">2n×2n$2n\times 2n$ matrix is diagonalizable under one of these transformations. In particular, we will give symplectic analogues of the singular value decomposition and the Takagi factorization.