norm                 package:Matrix                 R Documentation

_M_a_t_r_i_x _N_o_r_m_s

_D_e_s_c_r_i_p_t_i_o_n:

     Computes a matrix norm of 'x' using Lapack.  The norm can be the
     one norm, the infinity norm, the Frobenius norm, or the maximum
     modulus among elements of a matrix, as determined by the value of
     'type'.

_U_s_a_g_e:

     norm(x, type, ...)

_A_r_g_u_m_e_n_t_s:

       x: a real or complex matrix. 

    type: A character indicating the type of norm desired.

          '"_O"', '"_o"' _o_r '"_1"' specifies the one norm, (maximum
               absolute column sum);

          '"_I"' _o_r '"_i"' specifies the infinity norm (maximum absolute
               row sum);

          '"_F"' _o_r '"_f"' specifies the Frobenius norm (the Euclidean
               norm of 'x' treated as if it were a vector); and

          '"_M"' _o_r '"_m"' specifies the maximum modulus of all the
               elements in 'x'.

          The default is '"O"'.  Only the first character of 'type[1]'
          is used. 

     ...: further arguments passed to or from other methods.

_D_e_t_a_i_l_s:

     For dense matrices, the methods eventually call the Lapack
     functions 'dlange', 'dlansy', 'dlantr', 'zlange', 'zlansy', and
     'zlantr'.

_V_a_l_u_e:

     A numeric value of class '"norm"', representing the quantity
     chosen according to 'type'.

_R_e_f_e_r_e_n_c_e_s:

     Anderson, E., et al. (1994). _LAPACK User's Guide,_ 2nd edition,
     SIAM, Philadelphia.

_E_x_a_m_p_l_e_s:

     x <- Hilbert(9)
     norm(x, "1")
     norm(x, "I")
     norm(x, "F")
     norm(x, "M")

