Meaning of Hermitian matrix | Babel Free

Definitions

A square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that A=A^†.

Equivalents

Examples

“Hermitian matrices have real diagonal elements as well as real eigenvalues.”

“If a Hermitian matrix has a simple spectrum (of eigenvalues) then its eigenvectors are orthogonal.”

“If an observable can be described by a Hermitian matrix H, then for a given state #92;langleA#92;rangle, the expectation value of the observable for that state is #92;langleA#124;H#124;A#92;rangle.”

“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).”

“where H is a hermitian matrix. Now any linear combination of hermitian matrices with real coefficients is again a hermitian matrix.”

“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.”

CEFR level