Definition, Betydelse & Synonymer | Engelska ordet SELF-ADJOINT

Definition av SELF-ADJOINT

1. (matematik) självadjungerad

Exempel på hur man kan använda SELF-ADJOINT i en mening

• In quantum mechanics their importance lies in the Dirac–von Neumann formulation of quantum mechanics, in which physical observables such as position, momentum, angular momentum and spin are represented by self-adjoint operators on a Hilbert space.
• That theory was based in turn on the theory of projection-valued measures for self-adjoint operators that had been recently developed (by von Neumann and independently by Marshall Stone) and the Hilbert space formulation of quantum mechanics (attributed by von Neumann to Paul Dirac).
• In quantum mechanics, observables manifest as self-adjoint operators on a separable complex Hilbert space representing the quantum state space.
• mappings from physical observables (self-adjoint elements of the C*-algebra) to their expected measurement outcome (real number).
• Specifically, it shows that if M is a unital, self-adjoint operator algebra in the C*-algebra B(H), for some Hilbert space H, then the weak closure, strong closure and bicommutant of M are equal.
• However, some partial results have been established: for instance, any self-adjoint operator on an infinite-dimensional real Hilbert space admits an AIHS, as does any strictly singular (or compact) operator acting on a real infinite-dimensional reflexive space.
• The polar decomposition for matrices generalizes as follows: if A is a bounded linear operator then there is a unique factorization of A as a product A = UP where U is a partial isometry, P is a non-negative self-adjoint operator and the initial space of U is the closure of the range of P.
• It formalizes the idea that not all self-adjoint operators are observables because the relative phase of a superposition of nonzero states from different irreducible components is not observable (the expectation values of the observables can't distinguish between them).
• In functional analysis, the Friedrichs extension is a canonical self-adjoint extension of a non-negative densely defined symmetric operator.
• The even part of the star Lie superalgebra is the direct sum of the Poincaré algebra and a reductive Lie algebra B (such that its self-adjoint part is the tangent space of a real compact Lie group).
• In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent sums or products, and in particular can be used to define determinants and traces of some self-adjoint operators.
• The Hecke operators, which act on the space of all cusp forms, preserve the subspace of newforms and are self-adjoint and commuting operators (with respect to the Petersson inner product) when restricted to this subspace.
• While the extension problem for general symmetric operators is essentially that of extending partial isometries to unitaries, for positive symmetric operators the question becomes one of extending contractions: by "filling out" certain unknown entries of a 2 × 2 self-adjoint contraction, we obtain the positive self-adjoint extensions of a positive symmetric operator.
• These projections are bounded, self-adjoint, idempotent operators that satisfy the orthogonality condition.
• This operator is invertible, and its inverse is compact and self-adjoint so that the usual spectral theorem can be applied to obtain the eigenspaces of Δ and the reciprocals 1/λ of its eigenvalues.
• We now depart from the standard situation and present a general method of construction of coherent states, starting from a few observations on the structure of these objects as superpositions of eigenstates of some self-adjoint operator, as was the harmonic oscillator Hamiltonian for the standard CS.
• The BKM is truly meshfree, spectral convergent (numerical observations), symmetric (self-adjoint PDEs), integration-free, and easy to learn and implement.
• Since T* is formally self-adjoint on this inner product space, it follows immediately that any generalized eigenfunction of T* must already be an eigenfunction.
• The only simple algebra that can arise as the homomorphic image of a purely exceptional JB algebra is the Albert algebra, the 3 by 3 self-adjoint matrices over the octonions.

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