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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hermitian matrix ： ウィキペディア英語版 Hermitian matrix In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex entries that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and : :$a\_\; =\; \backslash overline\}$, in matrix form. Hermitian matrices can be understood as the complex extension of real symmetric matrices. If the conjugate transpose of a matrix $A$ is denoted by $A^\backslash dagger$, then the Hermitian property can be written concisely as :$A\; =\; A^\backslash dagger.$ Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having real eigenvalues. == Examples == See the following example: :$$ \begin 2 & 2+i & 4 \\ 2-i & 3 & i \\ 4 & -i & 1 \\ \end The diagonal elements must be real, as they must be their own complex conjugate. Well-known families of Pauli matrices, Gell-Mann matrices and their generalizations are Hermitian. In theoretical physics such Hermitian matrices are often multiplied by imaginary coefficients,〔 〕〔 (Physics 125 Course Notes ) at California Institute of Technology 〕 which results in ''skew-Hermitian'' matrices (see below). Here we offer another useful Hermitian matrix using an abstract example. If a square matrix $A$ equals the multiplication of a matrix and its conjugate transpose, that is, $A=BB^\backslash dagger$, then $A$ is a Hermitian positive semi-definite matrix. Furthermore, if $B$ is row full-rank, then $A$ is positive definite. 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 matrix」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.