linear_algebra: Finds the basis of the (right) null space.

In r-cas/caracas: Computer Algebra

Finds the basis of the (right) null space.

Description

Finds the basis of the (right) null space of a matrix, a vector (a 1-column matrix) or a model object for which a model matrix can be extracted. I.e. finds basis for the (right) null space x : Mx = 0.

Usage

is_caracas_matrix(M)

basis_intersect(M, M2)

basis_orthcomp(M, M2 = NULL)

basis_col(M)

basis_row(M)

basis_null(M)

basis_leftnull(M)

rref(M)

Arguments

M, M2

A matrix or a vector (a 1-column matrix).

Value

A matrix (possibly with zero columns if the null space consists only of the zero vector).

Author(s)

Søren Højsgaard, [e-mail]

See Also

Null

Examples

M <- matrix(c(1,1,1,1,1,1,0,0,0,0,1,1), nrow=4)
basis_null(M)
MASS::Null(t(M))

M <- matrix(c(1,1,1,1))
basis_null(M)
MASS::Null(t(M))

m0 <- lm(breaks ~ wool + tension, data=warpbreaks)
basis_null(model.matrix(m0))
MASS::Null(t(model.matrix(m0)))

## Make balanced dataset
dat.bal   <- expand.grid(list(A=factor(1:2), B=factor(1:3), C=factor(1:3)))
dat.bal$y <- rnorm(nrow(dat.bal))

## Make unbalanced dataset: 'B' is nested within 'C' so B=1 is only
## found when C=1 and B=2,3 are found in each C=2,3,4
dat.nst <- dat.bal
dat.nst$C <-factor(c(1,1,2,2,2,2,1,1,3,3,3,3,1,1,4,4,4,4))
xtabs(y ~ C+B+A , data=dat.nst)

mod.bal  <- lm(y ~ A + B*C, data=dat.bal)
mod.nst  <- lm(y ~ A + B*C, data=dat.nst)

basis_null( model.matrix(mod.bal) )
basis_null( model.matrix(mod.nst) )

MASS::Null( t(model.matrix(mod.bal)) )
MASS::Null( t(model.matrix(mod.nst)) )

r-cas/caracas documentation built on Feb. 28, 2025, 3:39 p.m.