norm               package:fUtilities               R Documentation

_M_a_t_r_i_x _N_o_r_m

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

     Returns the norm of a matrix.

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

     norm(x, p = 2)

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

       x: a numeric matrix. 

       p: an integer value, '1', '2' or 'Inf'. 'p=1' - The maximum
          absolute column sum norm which is defined  as the maximum of
          the sum of the absolute valued elements of columns  of the
          matrix. 'p=2' - The spectral norm is "the norm" of a matrix
          'X'.  This value is computed as the square root of the
          maximum eigenvalue  of 'CX' where 'C' is the conjugate
          transpose. 'p=Inf' - The maximum absolute row sum norm is
          defined  as the maximum of the sum of the absolute valued
          elements of rows of the matrix. 

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

     The function 'norm' computes the norm of a matrix. Three choices 
     are possible: 

     'p=1' - The maximum absolute column sum norm which is defined  as
     the maximum of the sum of the absolute valued elements of columns 
     of the matrix. 

     'p=2' - The spectral norm is "the norm" of a matrix 'X'.  This
     value is computed as the square root of the maximum eigenvalue  of
     'CX' where 'C' is the conjugate transpose.

     'p=Inf' - The maximum absolute row sum norm is defined  as the
     maximum of the sum of the absolute valued elements of rows of the
     matrix.

_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                  
          
     ## Return the Norm of the Matrix:                      
        norm(P)                                                       

