Abstract
For a family of linear operators A(λ→):U→U over C that smoothly depend on parameters λ→=(λ1,…,λk), V.I. Arnold obtained the simplest normal form of their matrices relative to a smoothly depending on λ→ change of a basis in U. We solve the same problem for a family of linear operators A(λ→):U→U over R, for a family of pairs of linear mappings A(λ→):U→V,B(λ→):U→V over C and R, and for a family of pairs of counter linear mappings A(λ→):U→V,B(λ→):V→U over C and R.
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