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...

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...

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...

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...

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)...

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...

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)...

In mathematics, the Arthur–Selberg trace formula is a generalization of the Selberg trace formula from the group SL2 to arbitrary reductive groups over...

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...

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...

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...

than the space of trace class operators. Dixmier traces are examples of singular traces. Some applications of Dixmier traces to noncommutative geometry...

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...

}=\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...

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...

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...

Hilbert spaces and trace class operators, which are easier to understand. (On Hilbert spaces nuclear operators are often called trace class operators.) We...

Trace Lysette (born 2 October 1981) is an American actress whose most notable roles include Shea in the television series Transparent (2014–2019) and...

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...

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...

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...

"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...

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...

In mathematics, the Selberg trace formula, introduced by Selberg (1956), is an expression for the character of the unitary representation of a Lie group...

micronutrients. The two types of trace element in biochemistry are classed as essential or non-essential. An essential trace element is a dietary element...

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...

that the operator TK is a trace class operator and trace ⁡ ( T K ) = ∫ a b K ( t , t ) d t . {\displaystyle \operatorname {trace} (T_{K})=\int _{a}^{b}K(t...

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)...

Kalton, noticing the spectral condition of Weiss, characterised all trace class commutators. Kalton's result forms the basis for the modern characterisation...

Tracor, Inc. was a major North American defense electronics contractor which was acquired by Marconi Electronic Systems (MES), a subsidiary of General...