矩阵、矩阵束和反梯度矩阵束的最简极小泛形变
Simplest miniversal deformations of matrices, matrix pencils, and contragredient matrix pencils
AI总结：
本文构造了实矩阵族和矩阵束族在光滑相似变换下的最简规范形，简化了Galin和Edelman等人的规范形。
摘要：
V. I. Arnold [Russian Math. Surveys 26 (2) (1971) 29-43] 构造了依赖于参数的复 n×n 矩阵族在同样依赖于参数的光滑相似变换下的简单规范形。我们为依赖于参数的实矩阵族和矩阵束族构造了类似的规范形，简化了 D. M. Galin [Uspehi Mat. Nauk 27 (1) (1972) 241-242] 以及 A. Edelman, E. Elmroth, B. Kagstrom [Siam J. Matrix Anal. Appl. 18 (3) (1997) 653-692] 的规范形。
英文摘要：
V. I. Arnold [Russian Math. Surveys 26 (2) (1971) 29-43] constructed a simple normal form for a family of complex n-by-n matrices that smoothly depend on parameters with respect to similarity transformations that smoothly depend on the same parameters. We construct analogous normal forms for a family of real matrices and a family of matrix pencils that smoothly depend on parameters, simplifying their normal forms by D. M. Galin [Uspehi Mat. Nauk 27 (1) (1972) 241-242] and by A. Edelman, E. Elmroth, B. Kagstrom [Siam J. Matrix Anal. Appl. 18 (3) (1997) 653-692].
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