# Manuals/calci/SVF

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SVF (Matrix)

• is any set of values.

## Description

• This function shows the Singular value of a given matrix in descending order.
• In , is any matrix with array of values.
• Singular value decomposition is defined by the factorization of a real or complex matrix.
• It is the generalization of the Eigen decomposition of a symmetric matrix with positive eigen values to any mxn matrix through an extension of the polar decomposition.
• Singular value decomposition is of the form where is any square real or complex Unitary matrix of order .
• is a mxn rectangular diagonal matrix with non negative real numbers.
• V is also any square real or complex Unitary matrix of order nxn.
• The columns of U and V are called left Singular and right Singular vectors of the matrix.
• To find Singular Value Decomposition we have to follow the below rules:
```*The left-singular vectors of the matrix M are a set of orthonormal eigenvectors of MM∗.
*The right-singular vectors of M are a set of orthonormal eigenvectors of .
*The non-zero singular values of M (found on the diagonal entries of Σ) are the square roots of the non-zero eigenvalues of both  and .
```

Singular Values