Hermitian matrix
Contents
EnglishEdit
EtymologyEdit
Named after Charles Hermite (1822–1901), French mathematician.
PronunciationEdit
NounEdit
Hermitian matrix (plural Hermitian matrixes or Hermitian matrices)
 (linear algebra) a square matrix with complex entries that is equal to its own conjugate transpose, i.e., a matrix such that where denotes the conjugate transpose of a matrix A
 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 equaleigenvalue 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 .
SynonymsEdit
 (hermitian matrix): selfadjoint matrix
HyponymsEdit
TranslationsEdit
mathematics: square matrix that is equal to its own conjugate transpose
