Ordinary Differential Equations and Dynamical Systems Vol2 · Problem 2.9

Existence Theory

Mathematics — Calculus · anti-symmetric-matrix-exponential

Problem

(a) Suppose that

A

is an anti-symmetric

n \times n

matrix over

\mathbb{R}

. Show that

\|\exp At\, x\| = \|x\|

, for all

x \in \mathbb{R}^n

and all

t \in \mathbb{R}

. (b) Find the stable, center, and unstable subspaces of

A