| intsectbasis {lmreg} | R Documentation |
Basis of intersection of two column spaces
Description
Computes an orthonormal basis of the intersection of column spaces of two given matrices.
Usage
intsectbasis(A, B, tol1=sqrt(.Machine$double.eps), tol2=sqrt(.Machine$double.eps))
Arguments
A |
First matrix. |
B |
Second matrix with identical number of rows. |
tol1 |
A relative tolerance to detect zero singular values while computing generalized inverse, in case the matrix concerned is rank deficient (default = sqrt(.Machine$double.eps)). |
tol2 |
A tolerance to detect if there is any non-zero singular value of a 'parallel sum' matrix, without which the intersection space is null (default = sqrt(.Machine$double.eps)). |
Value
Returns a semi-orthogonal matrix with columns forming an orthonormal basis of the intersection of the column spaces of A and B.
Author(s)
Debasis Sengupta <shairiksengupta@gmail.com>, Jinwen Qiu <qjwsnow_ctw@hotmail.com>
References
Sengupta and Jammalamadaka (2019), Linear Models and Regression with R: An Integrated Approach.
Examples
A<-matrix(2,3,5)
B<-matrix(3,3,2)
intsectbasis(A,B, tol1=sqrt(.Machine$double.eps), tol2=1e-14)