Sentences with hermitian matrix
Hermitian matrix
H h - Hermitian matrices have real diagonal elements as well as real eigenvalues. [1]If a Hermitian matrix has a simple spectrum (of eigenvalues) then its eigenvectors are orthogonal. [2] On the other hand, a set of two or more eigenvectors with the same eigenvalue can be orthogonalized (e. g. , through the Gram–Schmidt process, since any linear combination of equal-eigenvalue eigenvectors will also be an eigenvector) and will already be orthogonal to other eigenvectors which have different eigenvalues. If an observable can be described by a Hermitian matrix , then for a given state , the expectation value of the observable for that state is .