  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].
