# Singular Value Decomposition for zero-diagonal symmetric matrix

Let's say a zero-diagonal $4\times4$ symmetric matrix, $$\begin{bmatrix} 0 & 1 & 3 & 3 \\ 1 & 0 & 3 & 3 \\ 3 & 3 & 0 & 1 \\ 3 & 3 & 1 & 0 \end{bmatrix}$$

Does anyone know how to obtain SVD from the above matrix mathematically? as $A = U W V^*$ Note: eigenvectors of $A^*A$ will make up $V$ with associate eigenvalues of the diagonal of $W^*W$. Similarly, $D^*D = U^*(WW^*)U$

Thank you very much!

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Perhaps this is a somewhat related question. –  Michael Hardy Mar 27 '12 at 15:16
Why do you want the singular value decomposition for an invertible, diagonalizable, square matrix? In any case, see Wikipedia. –  TMM Mar 27 '12 at 19:58