rk                package:fUtilities                R Documentation

_T_h_e _R_a_n_k _o_f _a _M_a_t_r_i_x

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

     Returns the rank of a matrix.

_U_s_a_g_e:

     rk(x, method = c("qr", "chol"))

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

       x: a numeric matrix. 

  method: a character string. For 'method = "qr"' the rank is computed
          as 'qr(x)\$rank', or alternatively for  'method="chol"' the
          rank is computed as 'attr(chol(x, pivot=TRUE), "rank")'. 

_D_e_t_a_i_l_s:

     The function 'rk' computes the rank of a matrix which is  the
     dimension of the range of the matrix corresponding to the number 
     of linearly independent rows or columns of the matrix, or to the 
     number of nonzero singular values. 

     The rank of a matrix is also named inear map.

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

     Golub, van Loan, (1996); _Matrix Computations_,  3rd edition.
     Johns Hopkins University Press.

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

     ## Create Pascal Matrix:
        P = pascal(5)
        P
        
     ## Compute the Rank:
        rk(P)
        rk(P, "chol")                                

