6'2 Diagonalization

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11132008
6.2 Diagonalization
P-1 A P D
A P D P-1
Theorem An nn matrix A is diagonalizable iff
there are n linearly independent eigenvectors of
A. The diagonalizing matrix P has the
eigenvectors as its columns the diagonal
elements of D are the eigenvalues associated with
the eigenvectors.
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Real Symmetric Matrices
Theorem The eigenvalues of a real symmetric
matrix of order n are all real and it has n
linearly independent eigenvectors so is
diagonalizable.
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We used MATLAB in class today