# Difference Eigenvector values in mathematica 9 and mathematica 10 [duplicate]

I have the following matrix;

matrix={{0.213052 - 5.52399*10^-18 I, 0.123451 + 0.215784 I,
0.0771636 + 0.298479 I}, {0.123451 - 0.215784 I,
0.328615 - 4.47928*10^-18 I,
0.367929 + 0.0925207 I}, {0.0771636 - 0.298479 I,
0.367929 - 0.0925207 I, 0.458333 - 8.30535*10^-18 I}}


when I found Eigenvectors[matrix] in Mathematica 9, it gave the following output;

{{0.117433 + 0.4424 I, 0.552311 + 0.14137 I,
0.682245 + 0. I}, {-0.131023 - 0.625986 I,
0.730765 + 0. I, -0.163119 + 0.174212 I}, {0.010945 -
0.617533 I, -0.372767 + 0.0446533 I, 0.691075 + 0. I}}


But when I found Eigenvectors[matrix] in Mathematica 10, it gave different output which is;

{{-0.117433 - 0.4424 I, -0.552311 - 0.14137 I, -0.682245 +
0. I}, {-0.367396 + 0.523493 I, -0.499467 - 0.533433 I,
0.238658 + 0. I}, {0.010945 - 0.617533 I, -0.372767 + 0.0446533 I,
0.691075 + 0. I}}


After all my calculations the out put obtained from Mathematica 9 gives correct final result.

How i can understand this problem? And how to handle it? Thanks.

The eigenvectors are defined up to an arbitrary complex constant. In other words, if $v_i$ is an eigenvector then $c_iv_i$ is the same eigenvector. Usually eigenvectors is normalized so $|c_i|=1$.

v9 = {{0.117433 + 0.4424 I, 0.552311 + 0.14137 I,
0.682245 + 0. I}, {-0.131023 - 0.625986 I,
0.730765 + 0. I, -0.163119 + 0.174212 I}, {0.010945 -
0.617533 I, -0.372767 + 0.0446533 I, 0.691075 + 0. I}};
v10 = {{-0.117433 - 0.4424 I, -0.552311 - 0.14137 I, -0.682245 +
0. I}, {-0.367396 + 0.523493 I, -0.499467 - 0.533433 I,
0.238658 + 0. I}, {0.010945 - 0.617533 I, -0.372767 + 0.0446533 I,
0.691075 + 0. I}};

Chop[v10/v9]
(* {{-1., -1., -1.}, {-0.683483 - 0.729965 I, -0.683485 -
0.729965 I, -0.683484 - 0.729965 I}, {1., 1., 1.}} *)

Abs[%]
(* {{1., 1., 1.}, {0.999999, 1., 1.}, {1., 1., 1.}} *)


So the eigenvectors are the same (0.999999 is due to small precision of the copy-paste)

• ybeltukov thanks. But in a lengthy code i desire the result of v9 while using mathematica 10. What is your kind advice on it? Commented Jan 21, 2015 at 16:11
• It doesnt make any difference to the solution Commented Jan 21, 2015 at 16:23