characteristic polynomial

1
an algorithm to generate the
characteristic polynomial for a 3x3 matrix
2
M
3
M
det M
The constant term is minus the determinant of
the matrix M.
4
M
det M
trace M
The coefficient of the ?2 term is minus the
trace of the matrix M . The trace of the matrix M
a e i.
5
M
det M
trace M
The coefficient of the ? term is

6
M
det M
trace M
The coefficient of the ? term is


7
M
det M
trace M
The coefficient of the ? term is


8
example
9
M
det M 45
The constant term is minus the determinant of
the matrix M 45
10
M
trace M11
45
The coefficient of the ?2 term is minus the
trace of the matrix M . The trace of the matrix M
a e i 11
11
M
45
11
The coefficient of the ? term is

12
M
45
11
The coefficient of the ? term is
9


13
M
45
11
The coefficient of the ? term is
9
9


14
M
39
45
11
The coefficient of the ? term is
9
9
21


15
M
39
45
11