# Finding SVD for a square, symmetric matrix?

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• December 6th 2008, 09:39 AM
SWForeigner
Finding SVD for a square, symmetric matrix?
Is there any special technique to find the SVD for a square, symmetric, 3x3 matrix?
• December 6th 2008, 11:17 AM
Opalg
The only technique I know is to find the eigenvalues and eigenvectors. The singular value decomposition of the square matrix A is the factorisation $A=P^{\,\textsc{t}}DP$, where D is the diagonal matrix whose entries are the eigenvalues of A, and P is the orthogonal matrix whose columns are the corresponding normalised eigenvectors.