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Show that V is an internal direct sum of the eigenspaces
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[QUOTE="member 587159, post: 6413533"] A bunch of ideas: Have you been able to show that ##L## is diagonalisable? Maybe can you find some conditions the eigenvalues must satisfy? For example, you have that ##\lambda## is an eigenvalue with eigenvector ##A\in M_n(\mathbb{R})## if ##\lambda A =A^T##. Taking determinants, what conditions do you obtain? Does this help to find some eigenvectors? Can you find a basis of eigenvectors? [/QUOTE]
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Show that V is an internal direct sum of the eigenspaces
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