Schur-class              package:Matrix              R Documentation

_C_l_a_s_s "_S_c_h_u_r" _o_f _S_c_h_u_r _M_a_t_r_i_x _F_a_c_t_o_r_i_z_a_t_i_o_n_s

_D_e_s_c_r_i_p_t_i_o_n:

     Class '"Schur"' is the class of Schur matrix factorizations. 
     These are a generalization of eigen value (or "spectral")
     decompositions for general (possibly asymmmetric) square matrices,
     see the 'Schur()' function.

_O_b_j_e_c_t_s _f_r_o_m _t_h_e _C_l_a_s_s:

     Objects of class '"Schur"' are typically created by 'Schur()'.

_S_l_o_t_s:

     '"Schur"' has slots

     '_T': Upper Block-triangular 'Matrix' object.

     '_Q': Square _orthogonal_ '"Matrix"'.

     '_E_V_a_l_u_e_s': numeric or complex vector of eigenvalues of 'T'.

     '_D_i_m': the matrix dimension: equal to 'c(n,n)' of class
          '"integer"'.

_E_x_t_e_n_d_s:

     Class '"MatrixFactorization"', directly.

_S_e_e _A_l_s_o:

     'Schur()' for object creation; 'MatrixFactorization'.

_E_x_a_m_p_l_e_s:

     showClass("Schur")
     Schur(M <- Matrix(c(1:7, 10:2), 4,4))
     ## Trivial, of course:
     str(Schur(Diagonal(5)))

     ## for more examples, see Schur()