Null Spaces of Matrices

Usage

Null(M)

Arguments

M Input matrix. A vector is coerced to a 1-column matrix.

Description

Given a matrix, M, find a matrix N giving a basis for the null space. That is t(N) %*% M is the zero and N has the maximum number of linearly independent columns.

Value

The matrix N with the basis for the null space, or an empty vector if the matrix M is square and of maximal rank.

References

Venables & Ripley, Chapter 2.

See Also

qr, qr.Q

Examples

# The function is currently defined as
function(M)
{
	tmp <- qr(M)
	set <- if(tmp$rank == 0) 1:ncol(M) else  - (1:tmp$rank)
	qr.Q(tmp, complete = T)[, set, drop = F]
}


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