Graduate Why are the eigenvectors of this hermitian matrix not orthogonal?

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The discussion centers on the orthogonality of eigenvectors from a Hermitian matrix, despite having distinct eigenvalues. The user expresses frustration with repeated miscalculations from ChatGPT and their own inability to demonstrate orthogonality. The community emphasizes the importance of providing calculations in LaTeX for clarity and encourages users to verify their work independently rather than relying on AI tools.

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rghurst
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TL;DR
I am unable to show that the eigenvectors are orthogonal.
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.
 

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rghurst said:
TL;DR Summary: I am unable to show that the eigenvectors are orthogonal.

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.
Don't rely on ChatGPT and please repost your calculation attempt in LaTeX so it's readable and quotable.
 
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