Singular Value Decomposition of a Matrix

Singular Value Decomposition of a Matrix

Usage

svd2(x, rank = Inf)

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:

d

A vector containing the singular values of x, of length rank, sorted decreasingly.

u

A matrix whose columns contain the left singular vectors of x. Dimension c(m, rank).

v

A 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.