powerofpsdmatrix        package:compositions        R Documentation

_p_o_w_e_r _t_r_a_n_s_f_o_r_m _o_f _a _m_a_t_r_i_x

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

     Computes a power of a positive semidefinite symmetric matrix.

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

               powerofpsdmatrix( M , p,...)
               

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

       M: a Matrix, preferably symmetric

       p: a single number giving the power

     ...: further arguments to the singular value decomposition

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

     for a symmetric matrix the computed result can actually be
     considered as a version of the given power of the matrix
     fullfilling the relation:

                            M^pM^q=M^{p+q}

     The symmetry of the matrix is not checked.

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

     'U%*% D^p %*% t(P)' where the 'UDP' is a singular value
     decomposition of M.

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

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

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

     data(SimulatedAmounts)
     d <- ilr(sa.lognormals)
     var( d %*% powerofpsdmatrix(var(d),-1/2)) # Unit matrix

