Condition for a linear subspace

Reference no: EM13123948

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.

Reference no: EM13123948

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