octave: > A = [ 1, 2; 2, 1 ]
A =

  1  2
  2  1

octave: > p = poly( A )
p =

   1  -2  -3

octave: > roots( p )
ans =

   3
  -1

octave: > [ v, d ] = eig( A )
v =

  -0.70711   0.70711
   0.70711   0.70711

d =

  -1   0
   0   3

octave: > A * v./v
ans =

  -1   3
  -1   3