Pseudoinverse
The singular value decomposition can be used for computing the pseudoinverse of a matrix. Indeed, the pseudoinverse of the matrix M with singular value decomposition is
where Σ+ is the pseudoinverse of Σ, which is formed by replacing every nonzero diagonal entry by its reciprocal and transposing the resulting matrix. The pseudoinverse is one way to solve linear least squares problems.
Read more about this topic: Singular Value Decomposition, Applications of The SVD