A, P and D are n x n matrices. .. A is diagonalizable if and only if A has n eigenvalues, counting multiplicities. A is diagonalizable if A = PDP

' for some diagonal matrix D and some invertible matrix P. If there exists a basis for R" consisting entirely of eigenvectors of A, then A is diagonalizable. = If A is diagonalizable, then A is invertible.

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