Question:
Condition for a linear subspace E of R^n to be A-invariant
The exercise is as follows:
a) Let E be a linear subspace of R^n. Show that E is a closed subspace of R^n.
b) Let A be a real n x n matrix. Show that a linear subspace E of R^n is A-invariant if and only if E is e^{tA} -invariant for all t in R, where e^{tA} is the exponential matrix associated to A.