# Finding an eigenvector

• Feb 1st 2013, 01:09 PM
algorithm
Finding an eigenvector
Hi,

I'm trying to find an eigenvector of a matrix. I have λ = 1, so my matrix (A - λI) is
\$\displaystyle [-0.5253, 0.8593, -0.1906; -0.8612, -0.5018, 0.1010; 0.1817, 0.1161, -0.0236]\$

And from rows 2 and 3 I get these simultaneous equations

\$\displaystyle -0.8612t_{1}-0.5018t_{2}+0.1010t_{3}=0\$

\$\displaystyle 0.1817t_{1}+0.1161t_{2}-0.0236t_{3}=0\$

I eliminate to find \$\displaystyle t_{2}=0.225t_{3} \$ and \$\displaystyle t_{1}=-0.0137t_{3}\$

Thus the eigenvector is

t=\$\displaystyle k (-0.0137, 0.225, 1)\$

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

Thanks for any pointers.
• Feb 1st 2013, 02:45 PM
Deveno
Re: Finding an eigenvector
one question: are you using decimal approximations of rational numbers?
• Feb 1st 2013, 11:41 PM
algorithm
Re: Finding an eigenvector
Hi,

They're not approximations, just measurements.
• Feb 2nd 2013, 10:04 AM
algorithm
Re: Finding an eigenvector
Is my technique right?
• Feb 2nd 2013, 11:55 AM
ILikeSerena
Re: Finding an eigenvector
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.