Hermitian matrix

Etymology
Named after French mathematician (1822–1901), who demonstrated in 1855 that such matrices always have real eigenvalues.

Noun

 * 1)  A square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that $$A = A^\dagger.$$
 * 2) * 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).
 * 1) * 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.
 * 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.

Hyponyms

 * matrix
 * , matrix
 * matrix
 * , matrix

Translations

 * Czech: hermitovská matice
 * Finnish: hermiittinen matriisi
 * Icelandic: sjálfoka fylki, hermískt fylki
 * Italian: matrice hermitiana
 * Polish: macierz hermitowska
 * Russian: эрми́това ма́трица, самосопряжённая ма́трица