pascal              package:fUtilities              R Documentation

_P_a_s_c_a_l _M_a_t_r_i_x

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

     Creates a Pascal matrix.

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

     pascal(n)

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

       n: an integer value, the dimension of the square matrix. 

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

     The function 'pascal' generates a Pascal matrix of order 'n' 
     which is a symmetric, positive, definite matrix with integer
     entries  made up from Pascal's triangle. The determinant of a
     Pascal matrix is 1.  The inverse of a Pascal matrix has integer
     entries. If 'lambda'  is an eigenvalue of a Pascal matrix, then
     '1/lambda' is also an  eigenvalue of the matrix. Pascal matrices
     are ill-conditioned.

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

     Call G.S., Velleman D.J., (1993); _Pascal's matrices_,  American
     Mathematical Monthly 100, 372-376.

     Edelman A., Strang G., (2004); _Pascal Matrices_,  American
     Mathematical Monthly 111, 361-385.

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

     ## Create Pascal Matrix:
        P = pascal(5)
        P 
        
     ## Determinant
        det(pascal(5)) 
        det(pascal(10))   
        det(pascal(15))   
        det(pascal(20))                                       

