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

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

2007-10-04

arxiv.org/abs/0710.0946v1

Linear Algebra Appl. 302-303 (1999) 45-61

Mathematics

Representation Theory

20 pages

Scientific paper

10.1016/S0024-3795(99)00015-4

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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