Miniversal deformations of pairs of skew-symmetric matrices under congruence

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• 作者：Andrii Dmytryshyn ^{andrii@cs.umu.se" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A21 ; 15A63
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 October 2016
• 年：2016
• 卷：506
• 期：Complete
• 页码：506-534
• 全文大小：501 K

文摘

Miniversal deformations for pairs of skew-symmetric matrices under congruence are constructed. To be precise, for each such a pair eada25da5118318c42" title="Click to view the MathML source">(A,B)$(A,B)$ we provide a normal form with a minimal number of independent parameters to which all pairs of skew-symmetric matrices $(\tilde{A},\tilde{B})$, close to eada25da5118318c42" title="Click to view the MathML source">(A,B)$(A,B)$ can be reduced by congruence transformation which smoothly depends on the entries of the matrices in the pair $(\tilde{A},\tilde{B})$. An upper bound on the distance from such a miniversal deformation to eada25da5118318c42" title="Click to view the MathML source">(A,B)$(A,B)$ is derived too. We also present an example of using miniversal deformations for analyzing changes in the canonical structure information (i.e. eigenvalues and minimal indices) of skew-symmetric matrix pairs under perturbations.