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arXiv · 0710.0946

Simplest miniversal deformations of matrices, matrix pencils, and contragredient matrix pencils

M. Isabel Garcia-Planas·Vladimir V. Sergeichuk
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Abstract

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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BibTeXRIS

M. Isabel Garcia-Planas, Vladimir V. Sergeichuk. 2007-10-04. Simplest miniversal deformations of matrices, matrix pencils, and contragredient matrix pencils. https://doi.org/10.1016/s0024-3795(99)00015-4

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