Null: Null Spaces of Matrices

Description Usage Arguments Details Value References See Also Examples

View source: R/misc.R

Description

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 all-zero matrix and N has the maximum number of linearly independent columns.

Usage

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Null(M)

Arguments

M

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

qr, qr.Q.

Examples

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# 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]
}

Example output

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]
}

MASS documentation built on May 3, 2021, 5:08 p.m.

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