compbasis {lmreg}

Basis of orthogonal complement of column space of a matrix

Description

Computes an orthonormal basis of the orthogonal complement of the column space of a given matrix.

Usage

compbasis(M, tol=sqrt(.Machine$double.eps))

Arguments

M

Matrix for which basis of the orthogonal complement of the column space is needed.

tol

A relative tolerance to determine rank through qr decomposition
(default = sqrt(.Machine$double.eps)).

Value

Returns a semi-orthogonal matrix with columns forming an orthonormal basis of the orthogonal complement of the column space of M.

Author(s)

Debasis Sengupta <[e-mail]>, Jinwen Qiu <[e-mail]>

References

Sengupta and Jammalamadaka (2019), Linear Models and Regression with R: An Integrated Approach.

Examples

compbasis(matrix(c(3,3,3,3),2,2))