English

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

Representation Theory 2007-10-05 v1 Classical Analysis and ODEs Numerical Analysis

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].

Keywords

Cite

@article{arxiv.0710.0946,
  title  = {Simplest miniversal deformations of matrices, matrix pencils, and contragredient matrix pencils},
  author = {M. Isabel Garcia-Planas and Vladimir V. Sergeichuk},
  journal= {arXiv preprint arXiv:0710.0946},
  year   = {2007}
}

Comments

20 pages