Maxima: Eigenvectors output

Question

So I solve the eigenvectors for a matrix in Maxima.

a:matrix([10,10],[-4,-3]);
\\outputs matrix
vec:eigenvectors(a);
[[[5,2],[1,1]],[[[1,-1/2]],[[1,-4/5]]]]

I've hand calculated the eigenvalues, and vectors as (1x2) 5: [-2,1]. 2:[-5,4], which are correct. What is Maxima outputting?

Answer 1

Eigenvectors are only determined up to a multiplicative constant. That is, if x is an eigenvector, then so is a*x where a is a scalar. I think if you look at your result and Maxima's result, you'll see that they are equivalent in that sense.

There are different normalization schemes. Looks like Maxima makes the first element 1. Another common scheme is to make the norm of the eigenvector equal to 1. Or one can just leave them unnormalized.