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 = TRUE)[, set, drop = FALSE]
}