Self-adjoint — In mathematics, an element x of a star algebra is self adjoint if x^*=x.A collection C of elements of a star algebra is self adjoint if it is closed under the involution operation. For example, if x^*=y then since y^*=x^{**}=x in a star algebra,… … Wikipedia
Self-adjoint operator — In mathematics, on a finite dimensional inner product space, a self adjoint operator is one that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose.… … Wikipedia
self-adjoint matrix — ermitinė matrica statusas T sritis fizika atitikmenys: angl. Hermitian matrix; self adjoint matrix vok. Hermite Matrix, f; hermitesche Matrix, f; selbstadjungierte Matrix, f rus. самосопряжённая матрица, f; эрмитова матрица, f pranc. matrice… … Fizikos terminų žodynas
self-adjoint — adjective which is adjoint to itself … Wiktionary
self-adjointness — noun The condition of being self adjoint … Wiktionary
Hermitian adjoint — In mathematics, specifically in functional analysis, each linear operator on a Hilbert space has a corresponding adjoint operator. Adjoints of operators generalize conjugate transposes of square matrices to (possibly) infinite dimensional… … Wikipedia
Conjugate transpose — Adjoint matrix redirects here. For the classical adjoint matrix, see Adjugate matrix. In mathematics, the conjugate transpose, Hermitian transpose, Hermitian conjugate, or adjoint matrix of an m by n matrix A with complex entries is the n by m… … Wikipedia
Extensions of symmetric operators — In functional analysis, one is interested in extensions of symmetric operators acting on a Hilbert space. Of particular importance is the existence, and sometimes explicit constructions, of self adjoint extensions. This problem arises, for… … Wikipedia
Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… … Wikipedia
Compact operator on Hilbert space — In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… … Wikipedia
Borel functional calculus — In functional analysis, a branch of mathematics, the Borel functional calculus is a functional calculus (that is, an assignment of operators from commutative algebras to functions defined on their spectrum), which has particularly broad… … Wikipedia
