Eigenvector mystery

[John Keith]

I was just looking at the documentation for the Julia programming language today and I noticed something interesting.

In the second gray box on this page there is an example showing the calculation of eigenvectors and eigenvalues. I tried the same matrix on the HP 50 in approximate mode and the result for the eigenvectors was substantially different.

Wondering which set of eigenvectors was correct, I checked with Wolfram Alpha, which gave a third, completely different result! Going back to the 50g I tried the same matrix in exact mode, and obtained yet another result different from the previous 3. The eigenvalues in all 4 cases were the same however. The matrix is

Code:


[[ -4  -17
 [  2    2]]

Is this matrix so ill-conditioned that its eigenvectors can't be computed accurately? It doesn't seem so, its determinant is 26.