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

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].

20 pages

Cited by in corpus (6)

• Miniversal deformations of matrices of bilinear forms
• Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence
• Miniversal deformations of matrices under *congruence and reducing transformations
• Perturbation analysis of a matrix differential equation $\dot{x}=ABx$
• Generic families of matrix pencils and their bifurcation diagrams
• Neighborhood radius estimation for Arnold's miniversal deformations of complex and $p$-adic matrices