# Null

0th

Percentile

##### Null Spaces of Matrices

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.

Keywords
algebra
##### Usage
Null(M)
##### Arguments
M
Input matrix. A vector is coerced to a 1-column matrix.
##### 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, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

qr, qr.Q.

• Null
##### 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]
}
Documentation reproduced from package MASS, version 7.3-20, License: GPL-2 | GPL-3

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