Thread: Finding an eigenvector

Hi,


I'm trying to find an eigenvector of a matrix. I have λ = 1, so my matrix (A - λI) is



And from rows 2 and 3 I get these simultaneous equations





I eliminate to find and

Thus the eigenvector is

t=

But the actual answer is given as (-0.0088, 0.216, 1).

Thanks for any pointers.

one question: are you using decimal approximations of rational numbers?

Hi,

They're not approximations, just measurements.

Is my technique right?

Looks like you are having rounding errors.

When I calculate the eigenvector for the matrix you give, I'm getting different results than either of your answers.
See for instance here: {{1-0.5253, 0.8593, -0.1906},{ -0.8612, 1-0.5018, 0.1010},{ 0.1817, 0.1161, 1-0.0236}} - Wolfram|Alpha Results
The rounding errors you have are propagating more than you may like.

To answer your question: yes, your technique is right.
Note that there are more advanced methods to keep the rounding errors to a minimum.

Thanks very much for confirming. I've used more accurate values and I get a more sensible answer, still not spot-on though. Important thing is that my method is right.