myorth           package:ffmanova           R Documentation(latin1)

_R_a_n_k _a_n_d _o_r_t_h_o_n_o_r_m_a_l _b_a_s_i_s

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

     'myorth(X)' makes an orthonormal basis for the space spanned by
     the columns of 'X'. The number of columns returned equals
     'myrank(X)', which is the rank of 'X'.

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

     myorth(X, tol_ = 1e-09)
     myrank(X, tol_ = 1e-9)

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

       X: numeric matrix.

    tol_: tuning parameter for the rank.

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

     The calculations are based on the singular value decomposition
     ('svd'). And 'myrank(X)' is the number of singular values of 'X'
     that are larger than 'max(dim(X))*svd(x)$d[1]*tol_'.

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

     'myorth' returns a matrix, whose columns form an orthonormal
     basis.

     'myrank' returns a single number, which is the rank of 'X'.

_N_o_t_e:

     In the special case where 'X' has a single column, 'myorth(X)'
     returns 'c*X' where 'c' is a positive constant.

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

     yvind Langsrud and Bjrn-Helge Mevik

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

     'svd'

