1
$\begingroup$

consider this:

{Last@Eigensystem[{{0.0, 1.0}, {-2.0, -3.0}}], Eigenvectors[{{0.0, 1.0}, {-2.0, -3.0}}]}
(*{{{-0.447214, 0.894427}, {0.707107, -0.707107}}, {{-0.447214,0.894427}, {0.707107, -0.707107}}}*)

now with integer values:

{Last@Eigensystem[{{0, 1}, {-2, -3}}], Eigenvectors[{{0, 1}, {-2, -3}}]}
(*{{{-1, 2}, {-1, 1}}, {{-1, 2}, {-1, 1}}}*)

We get two different results. I understand that a single eigenvalue can correspond to multiple eigenvectors but at least there should be some consistency in the outputs (whether members are real values or integers).

I have noticed the same behaviour of both functions on 12.0 and 11.3.

$\endgroup$
4
  • 1
    $\begingroup$ The two results differ only by multiplicative factors. Eigenvectors are only defined by a direction, not a magnitude, so both are correct. $\endgroup$
    – Chris K
    Commented Oct 19, 2019 at 8:53
  • $\begingroup$ @ChrisK I understand that. But what i mean to say is that there should be some consistency in the output result. Why not output the same final result when either members are real or integers? $\endgroup$
    – Ali Hashmi
    Commented Oct 19, 2019 at 8:56
  • $\begingroup$ @ChrisK thanks for pointing it out ! $\endgroup$
    – Ali Hashmi
    Commented Oct 19, 2019 at 9:07
  • $\begingroup$ @ChrisK to be more specific, those are the unnormalized Eigenvectors (& Eigenvalues?) which occur when one uses exact values, correct? Using the second input here, one need only to add //N to the end of the given set of values to get the output from the first input. $\endgroup$ Commented Oct 19, 2019 at 15:19

0

Browse other questions tagged or ask your own question.