Ordinary Differential Equations and Dynamical Systems Vol2 · Problem 2.6

Existence Theory

Mathematics — Calculus · invariant-subspaces

Problem

Let AA be an n×nn \times n matrix over R\mathbb{R}, and let EsE_s, EuE_u, and EcE_c be its real stable, unstable, and center subspaces. (a) Prove that EsE_s, EuE_u, and EcE_c are invariant under AA. (b) Prove that EsE_s, EuE_u, and EcE_c are invariant under exp⁡At\exp At.

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