# Singular value decomposition

If matrix *A* has a matrix of eigenvectors **P** that is not invertible, then *A* does not have Eigen decomposition too. However, if *A* is an *m x n* real matrix with *m>n*, then the original matrix *A* can be written using a so-called singular value decomposition of the form (as the product of three matrices) *U*, *Σ*, *V**. Suppose we have the following matrix:

matrix = np.matrix([[6, 8],[5, 7]] )

Now the SVD can be computed by calling the `svd()`

method from the NumPy module of Python as follows:

**svd = np.linalg.svd(matrix)**

This is an array that has three fields–that is, `u`

, `sigma`

, and `v`

:

U = svd[0]Sigma = svd[1]V = svd[2]

For better interpretation of the preceding result, let's do some transformation–that is, converting each field ...

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