-->A
 A  =
 
!   4.    0.  - 2. !
! - 2.    2.    3. !
!   0.    0.    2. !
 
-->poly(A,'x')
 ans  =
 
                 2   3  
  - 16 + 20x - 8x + x   
 
-->v0
 v0  =
 
!   1. !
!   0. !
!   0. !
 
-->v1 = A*v0; v2 = A*v1; v3=A*v2; pv=[v0, v1, v2, v3]
 pv  =
 
!   1.    4.    16.    64. !
!   0.  - 2.  - 12.  - 56. !
!   0.    0.    0.     0.  !
 
-->rref(pv)
 ans  =
 
!   1.    0.  - 8.  - 48. !
!   0.    1.    6.    28. !
!   0.    0.    0.    0.  !
 
-->// poly x^2 - 6 x + 8 = (x-2)(x-4)
 
-->v1=(A-4*eye(3,3))*v0
 v1  =
 
!   0. !
! - 2. !
!   0. !
 
 
-->v2=(A-2*eye(3,3))*v1
 v2  =
 
!   0. !
!   0. !
!   0. !
 
-->// so v1 is eigenvector for eigenvalue 2.
 
-->A2=(A-2*eye(3))^3
 A2  =
 
!   44.  - 20.  - 76. !
! - 76.  - 12.    46. !
! - 20.  - 20.  - 12. !
 
-->A2=(A-2*eye(3,3))^3
 A2  =
 
!   8.    0.  - 8. !
! - 8.    0.    8. !
!   0.    0.    0. !
 
-->w0=[1 -1 0]'
 w0  =
 
!   1. !
! - 1. !
!   0. !
 
-->w1 = A*w0; w2 = A*w1; w3=A*w2; pw=[w0, w1, w2, w3]
 pw  =
 
!   1.    4.    16.    64. !
! - 1.  - 4.  - 16.  - 64. !
!   0.    0.    0.     0.  !
 
-->rref(pw)
 ans  =
 
!   1.    4.    16.    64. !
!   0.    0.    0.     0.  !
!   0.    0.    0.     0.  !
 
-->// poly is x-4
 
-->diary(0)