to compute the trace. This trace of trace-class operators generalizes the trace of matrices studied in linear algebra. All trace-class operators are compact...
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In mathematics, a weak trace class operator is a compact operator on a separable Hilbert space H with singular values the same order as the harmonic sequence...
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In linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...
37 KB (5,564 words) - 20:02, 25 May 2025
analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar-valued function on operators, the partial trace is an operator-valued...
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Look up Trace, trace, traces, or tracing in Wiktionary, the free dictionary. Trace may refer to: Trace (Son Volt album), 1995 Trace (Died Pretty album)...
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weak trace class is trace class. Consequently, every trace on the weak trace class ideal is singular and the co-dimension of the weak trace class ideal...
27 KB (3,733 words) - 10:20, 8 February 2024
operators on a Hilbert space which differ from the identity operator by a trace-class operator (i.e. an operator whose singular values sum up to a finite number)...
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In mathematics, the Arthur–Selberg trace formula is a generalization of the Selberg trace formula from the group SL2 to arbitrary reductive groups over...
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density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system. This...
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spaces such operators are usually called trace class operators and one can define such things as the trace. In Banach spaces this is no longer possible...
8 KB (1,268 words) - 01:16, 4 April 2023
Schatten–von-Neumann norm) arises as a generalization of p-integrability similar to the trace class norm and the Hilbert–Schmidt norm. Let H 1 {\displaystyle H_{1}} , H...
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than the space of trace class operators. Dixmier traces are examples of singular traces. Some applications of Dixmier traces to noncommutative geometry...
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generated by the Hermitian trace-class operators, with the trace norm. A mixed state ρ is separable if it can be approximated, in the trace norm, by states of...
6 KB (932 words) - 01:11, 23 December 2022
operators on an infinite dimensional Hilbert space we require that they be trace class and self-adjoint, in which case similar definitions apply, but we discuss...
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}=\left\|k\right\|_{2}} . The product of two Hilbert–Schmidt operators has finite trace-class norm; therefore, if A and B are two Hilbert–Schmidt operators, the Hilbert–Schmidt...
9 KB (1,391 words) - 23:43, 26 February 2025
Trace Lysette (born 2 October 1981) is an American actress whose most notable roles include Shea in the television series Transparent (2014–2019) and...
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Hilbert spaces and trace class operators, which are easier to understand. (On Hilbert spaces nuclear operators are often called trace class operators.) We...
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on a Hilbert space with unit trace. Mathematically, a quantum operation is a linear map Φ between spaces of trace class operators on Hilbert spaces H...
20 KB (2,831 words) - 21:20, 28 May 2024
theorem for traces explicitly identifies the commutant of a specific von Neumann algebra acting on a Hilbert space in the presence of a trace. The first...
20 KB (2,664 words) - 07:39, 27 December 2024
science, a trace is an equivalence class of strings, wherein certain letters in the string are allowed to commute, but others are not. Traces generalize...
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In mathematics, the Selberg trace formula, introduced by Selberg (1956), is an expression for the character of the unitary representation of a Lie group...
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Dimension (vector space) (section Trace)
"trace class operators" on a Hilbert space, or more generally nuclear operators on a Banach space. A subtler generalization is to consider the trace of...
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T_{\alpha }^{*}T_{\alpha }\to 0} in WOT. The predual of B(H) is the trace class operators C1(H), and it generates the w*-topology on B(H), called the...
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also mixed states are of importance; these are described by a positive trace-class operator ρ = ∑ i p i | ψ i ⟩ ⟨ ψ i | {\textstyle \rho =\sum _{i}p_{i}|\psi...
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example, the predual of the space of bounded operators is the space of trace class operators, and the predual of the space L∞(R) of essentially bounded...
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B {\displaystyle AB} (and hence, also B A {\displaystyle BA} ) is of trace class, det ( I m + A B ) = det ( I n + B A ) , {\displaystyle \det(I_{m}+AB)=\det(I_{n}+BA)...
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micronutrients. The two types of trace element in biochemistry are classed as essential or non-essential. An essential trace element is a dietary element...
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Commutator subspace (section Application to traces)
Kalton, noticing the spectral condition of Weiss, characterised all trace class commutators. Kalton's result forms the basis for the modern characterisation...
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H is the Banach space of all trace class operators with the trace norm ||A||= Tr(|A|). The Banach space of trace class operators is itself the dual of...
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Tracor, Inc. was a major North American defense electronics contractor which was acquired by Marconi Electronic Systems (MES), a subsidiary of General...
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