eigenvects function returning wrong answers for complex eigenvectors

[medwatt]

I was working on a problem and was getting funny results. I thought there was an issue with my matrices because I didn't expect the calculator to be giving wrong results.


Before, I present the issue, I want to point out that the function works fine for matrices with real eigenvalues/eigenvectors. In the last step, I'm using the matrix diagonalization formula.



This is the matrix I'm working on. It has two complex conjugate eigenvalues (and therefore eigenvectors). Because the eigenvector matrix returned is wrong, I wasn't able to get the original matrix using the matrix diagonalization formula, as was the case in the previous example.




If I manually enter the correct eigenvectors, I get the original matrix. This proves that the eigenvects function is returning wrong results when the eigenvectors are complex. The correct eigenvectors are shown in the "m" matrix.