英语词汇“hermitian conjugate”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

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.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [adjective] > of array > relating to matrices > qualities

adjoint1856

transposed1858

adjugate1867

orthogonal1891

alternant1892

positive definite1904

skew-symmetric1911

skew-symmetrical1911

unipotent1921

Hermitian1927

non-Hermitian1930

1927 Proc. Royal Soc. 1926–7 A. 113 628 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″) and b^—1(a″a′) are conjugate imaginaries, each matrix G will be Hermitian when the corresponding matrix g is Hermitian.

1935 P. A. M. Dirac Princ. Quantum Mech. (ed. 2) ii. 29 These are just the relations required for the matrix formed by the a_rs to be what is called a Hermitian matrix. A linear operator that satisfies this condition may conveniently be called a Hermitian operator.

1940 E. 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.

1951 J. A. Schouten Tensor Anal. for Physicists x. 241 For co- or contravariant hermitian tensors the following theorem holds.

1961 J. L. Powell & B. Crasemann Quantum Mech. ix. 295 Other matrices related to A = (a_ij), which occur frequently in the theory, are the transpose of A..and the Hermitian conjugate of A, A^† = (a*_ji).

1965 Czech. Math. Jrnl. 15 37 Let A, H be n-by-n hermitian matrices.

1967 G. 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.

1969 T. 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.

1973 Physics Bull. July 449/2 The analogous results for hermitean matrices.

单词	hermitian conjugate
释义	> as lemmas Hermitian conjugate 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. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [adjective] > of array > relating to matrices > qualities adjoint1856 transposed1858 adjugate1867 orthogonal1891 alternant1892 positive definite1904 skew-symmetric1911 skew-symmetrical1911 unipotent1921 Hermitian1927 non-Hermitian1930 1927 Proc. Royal Soc. 1926–7 A. 113 628 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″) and b^—1(a″a′) are conjugate imaginaries, each matrix G will be Hermitian when the corresponding matrix g is Hermitian. 1935 P. A. M. Dirac Princ. Quantum Mech. (ed. 2) ii. 29 These are just the relations required for the matrix formed by the a_rs to be what is called a Hermitian matrix. A linear operator that satisfies this condition may conveniently be called a Hermitian operator. 1940 E. 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. 1951 J. A. Schouten Tensor Anal. for Physicists x. 241 For co- or contravariant hermitian tensors the following theorem holds. 1961 J. L. Powell & B. Crasemann Quantum Mech. ix. 295 Other matrices related to A = (a_ij), which occur frequently in the theory, are the transpose of A..and the Hermitian conjugate of A, A^† = (a_ji). 1965 Czech. Math. Jrnl.* 15 37 Let A, H be n-by-n hermitian matrices. 1967 G. 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. 1969 T. 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. 1973 Physics Bull. July 449/2 The analogous results for hermitean matrices. extracted from Hermitianadj. < as lemmas
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> as lemmas