矩阵的块三角极小变形与矩阵束
Block triangular miniversal deformations of matrices and matrix pencils
摘要：
对于每个正方形复矩阵，V.I. Arnold构造了一个具有最小参数数的标准形，通过光滑地依赖于B的元素的相似变换，可以将与该矩阵足够接近的所有矩阵B族约简到该标准形。对于复矩阵束族，A. Edelman，E. Elmroth和B. Kagstrom和逆梯度矩阵束（即，矩阵对的变换（A，B）-->（S^{-1}AR，R^{-1}BS））通过M。I. Garcia-Planas和V.V. Sergeichuk。本文给出了矩阵族、矩阵束和逆矩阵束的其它标准形，我们的标准形是块三角形。
英文摘要：
For each square complex matrix, V. I. Arnold constructed a normal form with the minimal number of parameters to which a family of all matrices B that are close enough to this matrix can be reduced by similarity transformations that smoothly depend on the entries of B. Analogous normal forms were also constructed for families of complex matrix pencils by A. Edelman, E. Elmroth, and B. Kagstrom, and contragredient matrix pencils (i.e., of matrix pairs up to transformations (A,B)-->(S^{-1}AR,R^{-1}BS)) by M. I. Garcia-Planas and V. V. Sergeichuk. In this paper we give other normal forms for families of matrices, matrix pencils, and contragredient matrix pencils; our normal forms are block triangular.
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