

Null(MASS)                                   R Documentation

_N_u_l_l _S_p_a_c_e_s _o_f _M_a_t_r_i_c_e_s

_D_e_s_c_r_i_p_t_i_o_n_:

     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.

_U_s_a_g_e_:

     Null(M)

_A_r_g_u_m_e_n_t_s_:

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

_V_a_l_u_e_:

     The matrix `N' with the basis for the null space, or an
     empty vector if the matrix `M' is square and of maximal
     rank.

_R_e_f_e_r_e_n_c_e_s_:

     Venables  Ripley, Chapter 2.

_S_e_e _A_l_s_o_:

     `qr', `qr.Q'

_E_x_a_m_p_l_e_s_:

     # 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]
     }

