Given the matrix
X
of size
n x
p, the problem is to compute the Singular Value Decomposition (SVD)
X =
UΣV t,
where
-
U is an orthogonal matrix of size
n x
n
- Σ is a rectangular diagonal matrix of size
n x
p with non-negative values on the diagonal, called singular values
- V t is an orthogonal matrix of size
p x
p
Columns of the matrices
U and
V are called left and right singular vectors, respectively.