Orthogonal matrix

[kidia]

Please any idea on this one,Given the symmetric matrix [math]

A=\begin{bmatrix}0&2&2\\2&0&2\\2&2&0\end{bmatrix}

[/math] Find an orthogonal matrix P so that [math]

PAP^{-1}

[/math] is a diagonal matrix.

[CPL.Luke]

he matrix P is formed by finding the orthonormal eigenvectors of the matrix, first find the eigenvectors, and then orthonormalize

 

for a symmetric matrix, all of the eigenvectors are orthogonal for unique eigenvalues.