翻訳と辞書 Words near each other ・ Hermite interpolation ・ Hermite Islands ・ Hermite normal form ・ Hermite number ・ Hermite polynomials ・ Hermite reciprocity ・ Hermite ring ・ Hermite spline ・ Hermite's cotangent identity ・ Hermite's identity ・ Hermite's problem ・ Hermite–Hadamard inequality ・ Hermite–Minkowski theorem ・ Hermitian adjoint ・ Hermitian connection ・ Hermitian function ・ Hermitian hat wavelet ・ Hermitian manifold ・ Hermitian matrix ・ Hermitian symmetric space ・ Hermitian variety ・ Hermitian wavelet ・ Hermits of Saint William ・ Hermits of St. John the Baptist ・ Hermits of the Most Blessed Virgin Mary of Mount Carmel ・ Hermitude ・ Hermival-les-Vaux ・ Hermle ・ Hermle AG ・ Hermle Clocks Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hermitian function ： ウィキペディア英語版 Hermitian function In mathematical analysis, a Hermitian function is a complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign: :$f(-x)\; =\; \backslash overline$ (where the overbar indicates the complex conjugate) for all $x$ in the domain of $f$. This definition extends also to functions of two or more variables, e.g., in the case that $f$ is a function of two variables it is Hermitian if :$f(-x\_1,\; -x\_2)\; =\; \backslash overline$ for all pairs $(x\_1,\; x\_2)$ in the domain of $f$. From this definition it follows immediately that: $f$ is a Hermitian function if and only if * the real part of $f$ is an even function, and * the imaginary part of $f$ is an odd function. == Motivation == Hermitian functions appear frequently in mathematics, physics, and signal processing. For example, the following two statements follow from basic properties of the Fourier transform: * The function $f$ is real-valued if and only if the Fourier transform of $f$ is Hermitian. * The function $f$ is Hermitian if and only if the Fourier transform of $f$ is real-valued. Since the Fourier transform of a real signal is guaranteed to be Hermitian, it can be compressed using the Hermitian even/odd symmetry. This, for example, allows the discrete Fourier transform of a signal (which is in general complex) to be stored in the same space as the original real signal. * If ''f'' is Hermitian, then $f\; \backslash star\; g\; =\; f$ *g. Where the $\backslash star$ is cross-correlation, and $$ * is convolution. * If both ''f'' and ''g'' are Hermitian, then $f\; \backslash star\; g\; =\; g\; \backslash star\; f$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hermitian function」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.