duplication               package:rggm               R Documentation

_A _d_u_p_l_i_c_a_t_i_o_n _m_a_t_r_i_x

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

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

     duplication(n)

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

       n: a positive integer

_V_a_l_u_e:

     A 'n*(n+1)/2' matrix with real values.

_A_u_t_h_o_r(_s):

     Masashi Miyamura

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

     Jan R. Magnus and Heinz Neudecker, (1999) _Matrix Differential
     Calculus with Applications in Statistics and Econometrics_, Second
     Edition, John Wiley & Sons

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

     'vech', 'duplication.inverse', 'elimination'

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

       m <- matrix(c(1, 2, 3,
                     2, 5, 6,
                     3, 6, 9),
                   3, 3)
       duplication(3) %*% vech(m) # identical to as.vector(m)

