Singular values of rectangular matrix

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can any one explain me the need for singular values of a matrix. Explanation with a practical example will be appreciated

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It has multiple applications as in the case of Applications of Singular Value Decomposition. The most used ones could be to compute matrix inverse and storing a large but low rank matrix by its "principal components".

If you are into numerical computations, Golub's Matrix Computations has a much more detailed explanation.