from
http://www.math.utexas.edu/pipermail/maxima/2012/030933.html
a : matrix([0.8,0.5],[0.2,0.5]);
How do I get Maxima to give me
eigenvectors
V(1)=(0.928477,0.371391), and v(2)=(-0.707107,0.707107) ?
************************************************
(%i1) A : matrix([0.8,0.5],[0.2,0.5]);
(%o1) matrix([0.8,0.5],[0.2,0.5])
(%i2) ratprint:false$
(%i3) load(eigen);
(%o3)
"C:/PROGRA~2/MAXIMA~1.0-2/share/maxima/5.28.0-2/share/matrix/eigen.mac"
(%i4) A : matrix([0.8,0.5],[0.2,0.5]);
(%o4) matrix([0.8,0.5],[0.2,0.5])
(%i5) uniteigenvectors(A);
(%o5)
[[[3/10,1],[1,1]],[[[1/sqrt(2),-1/sqrt(2)]],[[5/sqrt(29),2/sqrt(29)]]]]
(%i6) float(%);
(%o6)
[[[0.3,1.0],[1.0,1.0]],[[[0.70710678118655,-0.70710678118655]],[[0.92847669088526,0.3713906763541]]]]
Other solution:
(%i7) eiv:eigenvectors(A);
(%o7) [[[3/10,1],[1,1]],[[[1,-1]],[[1,2/5]]]]
(%i8) v1:eiv[2][1][1];
(%o8) [1,-1]
(%i9) uvect(v1);
(%o9) [1/sqrt(2),-1/sqrt(2)]
(%i10) w1:float(%);
(%o10) [0.70710678118655,-0.70710678118655]
(%i11) v2:eiv[2][2][1];
(%o11) [1,2/5]
(%i12) w2:uvect(v2);
(%o12) [5/sqrt(29),2/sqrt(29)]
(%i13) w2:float(%);
(%o13) [0.92847669088526,0.3713906763541]
best
Aleksas D