Interval Analysis

Appendix

AProof of the Jordan normal form

The proof follows the lines in Filippov [96].

Proof. First we show the existence of a Jordan normal form.

Since A represents a linear mapping ϕ from some n dimensional linear space V into itself, we will base our proof on ϕ instead of A. We will show by induction on the dimension dim V = n of V that there is a basis {b¹,…,bⁿ} of V which either satisfies

or

Here λ is an eigenvector of ϕ, and bⁱ from (A.1) ...