singular value decomposition theorem

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

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Unformatted text preview: One of the most useful result from linear algebra is the singular value decomposition theorem. SVD Theorem: Let matrices of size entries, such that Recall that a matrix Let ̅ be a matrix of size and of size . of size , ∑ to consider ̂ (1) Let (2) Let , and assume that its rank is . Then there exist orthogonal , and a diagonal matrix of size with positive diagonal is said to be orthogonal if 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 [ [ ̅ ̅] ̅ . Compute the product be the identity matrix of size (3) Show that ̂ (4) Let has a svd: What is the size of the resulting matrix? . Compute . (5) (continued from (4)). Let corresponding columns of as given by the SVD Theorem above. Show that . Then we can use the columns of to represent the to achieve the dimension reduction. Show that and ...
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This note was uploaded on 01/16/2012 for the course MAD 4103 taught by Professor Li during the Spring '11 term at University of Central Florida.

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