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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 : :, in matrix form. Hermitian matrices can be understood as the complex extension of real symmetric matrices. If the conjugate transpose of a matrix is denoted by , then the Hermitian property can be written concisely as : 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: : 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 equals the multiplication of a matrix and its conjugate transpose, that is, , then is a Hermitian positive semi-definite matrix. Furthermore, if is row full-rank, then 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
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