Null
From MASS v7.345
by Brian Ripley
Null Spaces of Matrices
Given a matrix, M
, find a matrix N
giving a basis for the
(left) null space. That is crossprod(N, M) = t(N) %*% M
is an allzero matrix and N
has the maximum number of linearly
independent columns.
 Keywords
 algebra
Usage
Null(M)
Arguments
 M
 Input matrix. A vector is coerced to a 1column matrix.
Details
For a basis for the (right) null space
${x : Mx = 0}$,
use Null(t(M))
.
Value

The matrix
N
with the basis for the (left) null space, or a
matrix with zero columns if the matrix M
is square and of
maximal rank.
References
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.
See Also
Examples
library(MASS)
# The function is currently defined as
function(M)
{
tmp < qr(M)
set < if(tmp$rank == 0L) seq_len(ncol(M)) else seq_len(tmp$rank)
qr.Q(tmp, complete = TRUE)[, set, drop = FALSE]
}
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