Module 6: Dimensionality Reduction
Lecture 29: Singular Value Decomposition (SVD)
Singular Value Decomposition (SVD)
Factorization of a matrix
If A is of size
, then
is
,
is
and
is
matrix
Columns of
are eigenvectors of
Left singular vectors
(orthonormal)
Columns of
are eigenvectors of
Right singular vectors
(orthonormal)
are the singular values
is diagonal
Singular values are positive squareroots of eigenvalues of
or
(assuming
singular values)
, then 
is 
, 
is 
and 
is 
(orthonormal)
(orthonormal)
are the singular values
(assuming 
singular values)