Theorem 6.4

• Let A be an n?n matrix.

  • (a) If A has n linearly independent eigenvectors, it is diagonalizable. The matrix C whose columns consist of n linearly independent eigenvectors can be used in a similarity transformation C-1AC to give a diagonal matrix d. The diagonal elements of D will be the eigenvalues of A.
  • (b) If A is diagonalizable, then it has n linearly independent eigenvectors.

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