Hermitian matrix

== English == === Alternative forms === hermitian matrix === Etymology === Named after French mathematician Charles Hermite (1822–1901), who demonstrated in 1855 that such matrices always have real eigenvalues. === Pronunciation === (US) IPA(key): /hɝˈmɪ.ʃən ˈmeɪ.tɹɪks/ === Noun === Hermitian matrix (plural Hermitian matrixes or Hermitian matrices) (linear algebra) A square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that A = A † . {\displaystyle A=A^{\dagger }.} 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. ==== Hypernyms ==== normal matrix ==== Hyponyms ==== Pauli matrix Gramian matrix self-adjoint matrix symmetric matrix, real matrix ==== Translations ==== === References ===