singular value decomposition theorem

# singular value decomposition theorem - One of the most...

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One of the most useful result from linear algebra is the singular value decomposition theorem. SVD Theorem : Let be a matrix of size , and assume that its rank is . Then there exist orthogonal matrices of size and of size , and a diagonal matrix of size with positive diagonal entries, such that . Recall that a matrix of size is said to be orthogonal if . Let , Form the matrix [ ] . Define the mean vector ̅ to be ̅ In a lot of cases, we need to take the mean out of the data points which means we need

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