Rank and orthonormal basis

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Description

myorth(X) makes an orthonormal basis for the space spanned by the columns of X. The number of columns returned equals myrank(X), which is the rank of X.

Usage

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myorth(X, tol_ = 1e-09)
myrank(X, tol_ = 1e-9)

Arguments

X

numeric matrix.

tol_

tuning parameter for the rank.

Details

The calculations are based on the singular value decomposition (svd). And myrank(X) is the number of singular values of X that are larger than max(dim(X))*svd(x)$d[1]*tol_.

Value

myorth returns a matrix, whose columns form an orthonormal basis.

myrank returns a single number, which is the rank of X.

Note

In the special case where X has a single column, myorth(X) returns c*X where c is a positive constant.

Author(s)

Øyvind Langsrud and Bjørn-Helge Mevik

See Also

svd