skew-symmetric matrices对在同余下的微小变形
Miniversal deformations of pairs of skew-symmetric matrices under congruence
摘要：
构造了反对称矩阵对在同余下的极小变形。准确地说，对于每一个这样的一对$(A,B)$，我们提供了一个标准形式与最小数量的独立参数，所有对的反对称矩阵$(\widetilde{A},\widetilde{B})$，接近$(A,B)$可以减少的同余变换，顺利地依赖于在对$(\widetilde{A},\widetilde{B})$的矩阵的条目。导出了从这种微小变形到$(A,B)$的距离的上界。我们还提出了一个例子，使用minimums变形分析的正则结构信息（即特征值和最小指标）的反对称矩阵对扰动下的变化。
英文摘要：
Miniversal deformations for pairs of skew-symmetric matrices under congruence are constructed. To be precise, for each such a pair $(A,B)$ we provide a normal form with a minimal number of independent parameters to which all pairs of skew-symmetric matrices $(\widetilde{A},\widetilde{B})$, close to $(A,B)$ can be reduced by congruence transformation which smoothly depends on the entries of the matrices in the pair $(\widetilde{A},\widetilde{B})$. An upper bound on the distance from such a miniversal deformation to $(A,B)$ 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.
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