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An involution is a function f : X → X that, when applied twice, brings one back to the starting point. In mathematics, an involution, involutory function, or self-inverse function [1] is a function f that is its own inverse, f(f(x)) = x. for all x in the domain of f. [2] Equivalently, applying f twice produces the original value.
π(x) is a bounded linear operator since it is the direct sum of a family of operators, each one having norm ≤ ||x||. Theorem. The Gelfand–Naimark representation of a C*-algebra is an isometric *-representation. It suffices to show the map π is injective, since for *-morphisms of C*-algebras injective implies isometric.
Download as PDF; Printable version; In other projects ... This is an outline of topics related to linear algebra, the branch of mathematics concerning linear ...
If A represents a linear involution, then x→A(x−b)+b is an affine involution. One can check that any affine involution in fact has this form. Geometrically this means that any affine involution can be obtained by taking oblique reflections against any number from 0 through n hyperplanes going through a point b.
Description: Algebraic group: If k has characteristic ≠ 2, the special unitary group SU 2n/d (D,h), where D is a division algebra of degree d over k and h is a hermitian form of discriminant 1 and index r, relative to a k-linear involution σ of D, an "involution of the first kind such that the subring D σ has dimension d(d + 1)/2; or ...
Functional analysis applies the methods of linear algebra alongside those of mathematical analysis to study various function spaces; the central objects of study in functional analysis are L p spaces, which are Banach spaces, and especially the L 2 space of square integrable functions, which is the only Hilbert space among them. Functional ...
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In a dagger category , a morphism is called . unitary if † =,; self-adjoint if † =.; The latter is only possible for an endomorphism:.The terms unitary and self-adjoint in the previous definition are taken from the category of Hilbert spaces, where the morphisms satisfying those properties are then unitary and self-adjoint in the usual sense.
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