We answer the question how arbitrarily small perturbations of a pair of one arbitrary and one symmetric $2\times 2$ matrix can change a normal form with respect to a certain linear group action. This result is then applied to describe the quadratic part of normal forms of complex points of small ${\mathcal{C}}^2$-perturbations of real 4-manifolds embedded in a complex 3-manifold.

中文翻译：

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关于嵌入复杂3流形的实4流形的小𝒞2扰动的复点的范式

我们回答这个问题：一对任意和一个对称的一对的任意小的扰动 $2\times 2$矩阵可以相对于某些线性群作用改变正态形式。然后将该结果用于描述小点的复数点的正态形式的二次部分${\mathcal{C}}^2$-嵌入复杂的3流形的实4流形的扰动。