Singular Value Decomposition of a Matrix
Arguments
- x
A \(m \times p\) numeric matrix.
- rank
An integer value specifying the maximal number of components
to be kept in the results.
Value
A list with the following elements:
dA vector containing the singular values of x, of length
rank, sorted decreasingly.
uA matrix whose columns contain the left singular vectors of
x. Dimension c(m, rank).
vA matrix whose columns contain the right singular vectors of
x. Dimension c(p, rank).
Note
In both PCA and PCA-cor whitening there is a sign-ambiguity in the
eigenvector matrices. In order to resolve the sign-ambiguity we use
eigenvector matrices with a positive diagonal. This has the effect to make
cross-correlations and cross-correlations positive diagonal for PCA.
