Eigenvectors

[rawi]

DrD wrote:

Quote:a:=[[0.9,0.2], [0.1,0.8]]; Entries with approximate values
a1:=[[9/10,2/10], [1/10,8/10]]; The same matrix with exact values

eigenvects(a); ==> [[0.894427191,−0.7453559925],[0.4472135955,0.7453559925]];

// Using either of these:
eigenvects(exact(a));
eigenvects(a1); // ==> [[2,-1],[1,1]]; MUCH nicer to work with

Wolfram Alpha returns [[2,-1],[1,1]],

I do not see any problem here. All solutions are correct. If a vector a is an eigenvector as well c*a is an eigenvector with c being any real number different from zero.
The solution starting with .89 is a normalized solution with the length of the eigenvector being 1. The solution starting with 2 is not normalized but has the advantage of being an exact solution.

Best