I am just curious about it because my examples for my final assignment involve many positive definite matrix. When I want to unitary diagonalize a positive definite matrix, its eigenvectors already orthonormal. So, is it true that eigenvectors of every positive definite matrix are orthonormal? Or are there some conditions for the matrix so that the eigenvectors can be orthonormal? Or is it just my example?
Note : what I know is every hermitian matrix has orthogonal eigenvectors (corresponding with distinct eigenvalues).
Sorry I can't show my examples because of "bad" numbers (float numbers). And sorry for my bad english.
By definition, every positive definite matrix is symmetric. And eigenvectors corresponding to distinct eigenvalues of real symmetric matrices are always orthogonal.