How to ensure orthogonality of eigenvectors

[Chong_Wang]

I have a Hermitian matrix A. Due to numerical errors, (A'-A)/2 is around 10^-17 and eig returns nonorthogonal eigenvectors. I don’t see a eigh function (from numpy) counterpart in julia. How can I ensure orthogonality of eigenvectors of A?

[stevengj]

eig(Hermitian(A))

[Chong_Wang]

Thank you. Although it is a little bit inconvenient when A has imaginary part in its diagonal axis due to floating point error.

[rveltz]

You can rewrite the matrix by keeping only the upper part and copy this upper part to the lower part. This will be exactly symmetric.

[fredrikekre]

@Chong_Wang

Although it is a little bit inconvenient when A has imaginary part in its diagonal axis due to floating point error.

See Avoid checking the diagonal for non-real elements when constructing Hermitians by andreasnoack · Pull Request #17367 · JuliaLang/julia · GitHub