# strange behaviour of Eigensystem and Eigenvectors [duplicate]

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.

• The two results differ only by multiplicative factors. Eigenvectors are only defined by a direction, not a magnitude, so both are correct. Commented Oct 19, 2019 at 8:53
• @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? Commented Oct 19, 2019 at 8:56
• @ChrisK thanks for pointing it out ! Commented Oct 19, 2019 at 9:07
• @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. Commented Oct 19, 2019 at 15:19