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In mathematics, an element ''x'' of a *-algebra is self-adjoint if . A collection ''C'' of elements of a star-algebra is self-adjoint if it is closed under the involution operation. For example, if then since in a star-algebra, the set is a self-adjoint set even though ''x'' and ''y'' need not be self-adjoint elements. In functional analysis, a linear operator ''A'' on a Hilbert space is called self-adjoint if it is equal to its own adjoint ''A'' * and that the domain of ''A'' is the same as that of ''A'' *. See self-adjoint operator for a detailed discussion. If the Hilbert space is finite-dimensional and an orthonormal basis has been chosen, then the operator ''A'' is self-adjoint if and only if the matrix describing ''A'' with respect to this basis is Hermitian, i.e. if it is equal to its own conjugate transpose. Hermitian matrices are also called self-adjoint. In a dagger category, a morphism is called self-adjoint if ; this is possible only for an endomorphism . ==See also== *Symmetric matrix *Self-adjoint operator *Hermitian matrix 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「selfadjoint」の詳細全文を読む スポンサード リンク
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