Q {lazy.mat}

R Documentation

Projection Operators to the Orthogonal Complement of the Column Space of the Input

Description

Projection Operators to the Orthogonal Complement of the Column Space of the Input

Usage

Q(
  ...,
  Ginv = 0,
  Ginvargs = list(tol = .Machine$double.eps, MASS = 0, MP = 0, nopermute = 0, eps =
    1e-08, chkginv = 0, epsc = 1e-08)
)

Arguments

...	Input matrices: The projection operator to the column space of the column binded matices will be calculated.
Ginv	= 1 to use Ginv function in lazy.mat package
Ginvargs	The list of arguments to Ginv function

Details

Let X be the colum binded ... matrices.
The the projection operator to the orthogonal complement of the column space of X is defined as
I - X %*% solve( t(X) %*% X ) %*% t(X) .
If X is not of full column rank, native solve function stops with error. In this case, use Ginv=1 in order to replace solve with Ginv function.

Examples

X=demomat(3,2)
PX=P(X)
PX1=P(rep(1,nrow(X)),X, Ginv=1)
PX-PX1
QX=Q(X)
PX%*%QX

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