Singular value decomposition (SVD)
SVD decomposes any mxn matrix A as
Properties
•Σ is
a diagonal matrix containing the eigenvalues of ATA
–known
as “singular values” of A
–diagonal
entries are sorted from largest to smallest
•columns
of U are eigenvectors of AAT
•columns
of V are eigenvectors of ATA
If A is singular (e.g., has rank 3)
•only first 3 singular
values are nonzero
•we can throw away all
but first 3 columns of U and V
•Choose M’ = U’, S’ = Σ’V’T
