Trying to figure out what, exactly, maxima is returning when I use
eigenvectors. Take the following simple example:
a : matrix([0.8,0.5],[0.2,0.5]);
[vals,vecs] : float(eigenvectors(a));
Second command yields
[[[0.3,1.0],[1.0,1.0]],[[[1.0,-1.0]],[[1.0,0.4]]]]
The eigenvalues are 1, 0.3 (confirmed by other software - e.g., Maple,
MATLAB...)
But, the eigenvectors are given as 1,1,-1,4. In matrix form
e : transpose(apply('matrix,map('first,vecs)));
which yields
matrix([1.0,1.0],[-1.0,0.4])
Fine, except I can figure out how/why these are so different from what
other software generates - for the 3 applications I've tried (Maple,
MATLAB, Mathematica); I get
V(1)=(0.928477,0.371391), and v(2)=(-0.707107,0.707107).
Can somebody provide a quick explanation for what Maxima is reporting
for eigenvectors, which seems to be very* different from whatother CAS
gives? I suspect I'm missing something obvious. (Must be!).
Thanks very much in advance.