Suppose that $A$ is an $n\times n$ matrix such that $A^2 = I$. What can you say about the stability of the origin of the linear system $\dot{x} = Ax$? Are there nontrivial stable and/or unstable subspaces?
2026-03-28 03:27:28.1774668448
Stability of the origin of the linear system $\dot{x} = Ax$ given $A^2 = I$
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Hint: For a start, what can you say about the eigenvalues?