| 释义 |
Hermitian, a. Math.|hɜːˈmɪʃən|
Also herm-, -ean.
[ad. F. hermitien n. and adj. (L. Autonne 1902, in Rendiconti d. Circolo matem. XVI. 104), f. the name of C. Hermite (1822–1905), French mathematician: see -ian.]
Applied to a matrix in which pairs of elements symmetrically placed with respect to the principal diagonal are complex conjugates, and to other quantities (such as a self-adjoint operator of transformation, or a bilinear form) whose coefficients or elements form such a matrix; Hermitian conjugate, the complex conjugate of the transpose of a matrix.
1927Proc. R. Soc. A. CXIII. 628 If b commutes with H, the new matrix..will be a diagonal matrix, and if in addition the elements of the matrices b and b—1 satisfy the condition that b(a′a{pp}) and b—1(a{pp}a′) are conjugate imaginaries, each matrix G will be Hermitian when the corresponding matrix g is Hermitian. 1935P. A. M. Dirac Princ. Quantum Mech. (ed. 2) ii. 29 These are just the relations required for the matrix formed by the ars to be what is called a Hermitian matrix. A linear operator that satisfies this condition may conveniently be called a Hermitian operator. 1940E. T. Bell Devel. Math. xiv. 285 From Hermite's arithmetical theory of these forms..evolved the extensive theory of Hermitian forms and matrices, which after 1925 became familiar to physicists through the revised quantum theory. 1951J. A. Schouten Tensor Analysis for Physicists x. 241 For co- or contravariant hermitian tensors the following theorem holds. 1961Powell & Crasemann Quantum Mech. ix. 295 Other matrices related to A = (aij), which occur frequently in the theory, are the transpose of A,..and the Hermitian conjugate of A, A† = (a*ji). 1965Czech. Math. Jrnl. XV. 37 Let A, H be n-by-n hermitian matrices. 1967G. G. Hall Appl. Group Theory iii. 33 A less obvious example is that complex Hermitean 2 × 2 matrices form a four-dimensional real Euclidean space. 1969T. F. Jordan Linear Operators Quantum Mech. ii. 23 A Hermitian operator A is characterized by the equation (ϕ, Aψ) = (Aϕ, ψ) or (ϕ, Aψ) = (ψ, Aϕ)* holding for all vectors ψ and ϕ. 1973Physics Bull. July 449/2 The analogous results for hermitean matrices. |