[Vec,Val]=eig(A)
Vec =
0.7071 0.4472
-0.7071 0.8944
What does the eig function return? From its documentation: "[V,D] = eig(A) returns diagonal matrix D of eigenvalues and matrix V whose columns are the corresponding right eigenvectors, so that A*V = V*D." So is A*V close to V*D? A*Vec-Vec*Val
ans =
0 2.77555756156289e-17
0 0
Yeah, those are pretty close to 0. How about for your matrix of eigenvectors?
Perhaps, from the orientation of your eigenvectors, you're trying to use the left eigenvectors? "[V,D,W] = eig(A) also returns full matrix W whose columns are the corresponding left eigenvectors, so that W'*A = D*W'." [Vec, Val, VecLeft] = eig(A);
VecLeft
VecLeft =
0.894427190999916 0.707106781186547
-0.447213595499958 0.707106781186547
VecLeft'*A - Val*VecLeft'
Still no. So please show me why you believe that the columns of Vec2 are eigenvectors for this matrix.
If we scaled VecLeft a bit it looks a little similar to your Vec2 matrix but not exactly.
VecLeftScaled = VecLeft ./ VecLeft(2, :)
VecLeftScaled'*A-Val*VecLeftScaled'
Best Answer