charp SciMax Toolbox chebyshev_t

SciMax Toolbox >> charpoly

charpoly

Maxima Function

Calling Sequence

charpoly (M, x)

Description

Returns the characteristic polynomial for the matrix M with respect to variable x. That is, determinant (M - diagmatrix (length (M), x)).

(%i1) a: matrix ([3, 1], [2, 4]);
                            [ 3  1 ]
(%o1)                       [      ]
                            [ 2  4 ]
(%i2) expand (charpoly (a, lambda));
                           2
(%o2)                lambda  - 7 lambda + 10
(%i3) (programmode: true, solve (%));
(%o3)               [lambda = 5, lambda = 2]
(%i4) matrix ([x1], [x2]);
                             [ x1 ]
(%o4)                        [    ]
                             [ x2 ]
(%i5) ev (a . % - lambda*%, %th(2)[1]);
                          [ x2 - 2 x1 ]
(%o5)                     [           ]
                          [ 2 x1 - x2 ]
(%i6) %[1, 1] = 0;
(%o6)                     x2 - 2 x1 = 0
(%i7) x2^2 + x1^2 = 1;
                            2     2
(%o7)                     x2  + x1  = 1
(%i8) solve ([%th(2), %], [x1, x2]);
                  1               2
(%o8) [[x1 = - -------, x2 = - -------],
               sqrt(5)         sqrt(5)
                                             1             2
                                    [x1 = -------, x2 = -------]]
                                          sqrt(5)       sqrt(5)
charp SciMax Toolbox chebyshev_t