Recent content by rghurst

Awesome! Thanks for the explanation. I have understood this as a general rule for as long as I can remember, but I now have a much better intuitive understanding of the need to define the inner product this way for complex vectors. Now if I could only have a more intuitive grasp of...

Thank you for explaining this, but why does the rule change? In my mind, arbitrarily conjugating one of the eigenvectors makes another vector that is neither of the two actual eigenvectors. Do not the two actual eigenvectors as originally calculated have to be orthogonal? Perhaps the inner...

The eigenvectors of a hermitian matrix corresponding to unique eigenvalues are orthogonal. This is not too difficult of a statement to prove using mathematical induction. However, this case is seriously bothering me. Why is the dot product of the vectors not rightly zero? Is there something more...

Why are the eigenvectors of this hermitian matrix not checking out as orthogonal? The eigenvalues are certainly distinct. ChatGPT also is miscalculating repeatedly. I have checked my work many times and cannot find the error. Kindly assist.

This makes full sense to me now. Thanks.

Thanks. This makes better sense to me. I am still admittedly having a difficult time seeing why the series solution would not match exactly that provided by the characteristic polynomial.