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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](http://math.stackexchange.com/questions/54133/eigenvalues-of-certain-block-matrices) is a somewhat related question.2012-03-27
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    Why do you want the singular value decomposition for an invertible, diagonalizable, square matrix? In any case, see [Wikipedia](http://en.wikipedia.org/wiki/Singular_value_decomposition).2012-03-27
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    Your question is unclear. Are you looking for a singular value decomposition for the matrix in your question, or SVDs for a general class of matrices? Are you looking for some numerical methods, or some theoretical methods that allow you to hand-calculate the SVDs?2017-12-20

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