Hermitian matrix

English Alternative forms en hermitian matrix Etymology Named after French mathematician Charles Hermite (1822–1901), who demonstrated in 1855 that such matrices always have real eigenvalues. Pronunciation en /hɝˈmɪ.ʃən ˈmeɪ.tɹɪks/ US Noun + Hermitian matrices en linear algebra A square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that en Hermitian matrices have real diagonal elements as well as real eigenvalues. http://www.proofwiki.org/wiki/Hermitian_Operators_have_Real_Eigenvalues Proof Wiki — Hermitian Operators have Real Eigenvalues 14 January 2013 https://web.archive.org/web/20130325071301/http://www.proofwiki.org/wiki/Hermitian_Operators_have_Real_Eigenvalues 25 March 2013 en If a Hermitian matrix has a simple spectrum (of eigenvalues) then its eigenvectors are orthogonal. http://www.proofwiki.org/wiki/Hermitian_Operators_have_Orthogonal_Eigenvectors Proof Wiki — Hermitian Operators have Orthogonal Eigenvectors 15 January 2013 https://web.archive.org/web/20130325071237/http://www.proofwiki.org/wiki/Hermitian_Operators_have_Orthogonal_Eigenvectors 25 March 2013 en 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 . 1988, I. M. Gelfand, M. I. Graev, Geometry of homogeneous spaces, representations of groups in homogeneous spaces and related questions of integral geometry, Israel M. Gelfand, Collected Papers, Volume II, Springer-Verlag, page 366, There are three types of such spaces: the space of positive definite (or negative definite) Hermitian matrices, the space of nondefinite Hermitian matrices, and finally the space of degenerate Hermitian matrices p, satisfying the condition p ≥ 0 (or p ≤ 0). 1997, A. W. Joshi, Elements of Group Theory for Physicists, New Age International, 4th Edition, page 129, For this we note that if H is a hermitian matrix, exp(iH) is a unitary matrix. The converse is also true, i.e., if U is any unitary matrix, then it can be expressed in the form U = exp(iH),          (4.94) where H is a hermitian matrix. Now any linear combination of hermitian matrices with real coefficients is again a hermitian matrix. en 1998 Eugenio Iannone; Francesco Matera; Antonio Mecozzi; Marina Settembre Nonlinear Optical Communication Networks https://books.google.com.au/books?id=KgNTAAAAMAAJ&q=%22Hermitian+matrixes%22&dq=%22Hermitian+matrixes%22&hl=en&sa=X&ved=0ahUKEwintYKu8fzXAhUJfLwKHSm_DdwQ6AEIkgEwEg 442 Exploiting the properties of hermitian matrixes [2], it is possible to obtain an analytical expression for the characteristic function of a hermitian quadratic form of gaussian variables, which is useful in the evaluation of transmission system performance. Hypernyms en normal matrix Hyponyms en Pauli matrix en Gramian matrix en self-adjoint matrix en symmetric matrix, en real matrix Translations square matrix equal to its own conjugate transpose Czech: cs hermitovská matice f Finnish: fi hermiittinen matriisi Icelandic: is sjálfoka fylki n, is hermískt fylki n Italian: it matrice hermitiana f Polish: pl macierz hermitowska f Russian: ru эрми́това ма́трица f, ru самосопряжённая ма́трица f References en eponyms