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* @return[list] A list of two matrices: [P, D] such that D is diagonal and M = P . D . P^^-1. Returns empty list if M is not diagonalizable
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*/
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ddiagonalize(M):= block([P,D],
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diagonalize(M):= block([P,D],
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if not(squarep(M)) then return([]),
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[P, D]: get_Jordan_form(M),
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if ev(zeromatrixp(M - transpose(M)),simp) then P:ev(transpose(apply('matrix, map(lambda([ex], ex/sqrt(ex.ex)), gramschmidt(args(transpose(P)))))), simp),
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