Null                  package:MASS                  R Documentation

Null Spaces of Matrices

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.

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.

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]
     }

