Calculating the singular value decomposition of a matrix

Singular value decomposition (SVD) is one of the more useful techniques in typical data science techniques.

• One of the most important applications of SVD is in recommendation systems, where the matrix of user-item purchase behavior is broken into multiple matrices that are simpler to implement.
• Similarly, SVD is used in image compression algorithms, where we try to capture the information within algorithms by using as few pixels as possible.

The SVD of a matrix A is the decomposition or factorization of A into the product of three matrices: A=UxΣxVt.

The size of the individual matrices is as follows, if you know that matrix A is of size M x N:

• Matrix U is of size M x M
• Matrix V is of size N x N
• Matrix Σ is of size M x N

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