Trace operator information

In mathematics, the trace operator extends the notion of the restriction of a function to the boundary of its domain to "generalized" functions in a Sobolev...

specifically functional analysis, a trace-class operator is a linear operator for which a trace may be defined, such that the trace is a finite number independent...

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 function...

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)...

matrices and linear operators on Hilbert spaces. This article covers some important operator inequalities connected with traces of matrices. Let H n...

which is the operator norm induced by the vector 2-norm (see above). Finally, p = 1 yields the nuclear norm (also known as the trace norm, or the Ky...

In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean...

Arthur–Selberg trace formula. When Γ is the fundamental group of a Riemann surface, the Selberg trace formula describes the spectrum of differential operators such...

(\rho F_{i})} , where tr {\displaystyle \operatorname {tr} } is the trace operator. When the quantum state being measured is a pure state | ψ ⟩ {\displaystyle...

semi-definite, see below. In operator language, a density operator for a system is a positive semi-definite, Hermitian operator of trace one acting on the Hilbert...

{Tr} (\rho \ln \rho ),} where ρ is the density matrix, and Tr is the trace operator. This upholds the correspondence principle, because in the classical...

for particular kinds of operators. The Fredholm determinant defines the determinant for operators known as trace class operators by an appropriate generalization...

states) is described by a density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing...

dimension. In Hilbert spaces such operators are usually called trace class operators and one can define such things as the trace. In Banach spaces this is no...

force in 2002, making traceability compulsory for food and feed operators and requiring those businesses to implement traceability systems. The EU introduced...

Grothendieck trace theorem is an extension of Lidskii's theorem about the trace and the determinant of a certain class of nuclear operators on Banach spaces...

}}\gamma ({\vec {u}})=0\}} , where γ {\displaystyle \gamma } is the trace operator. Furthermore, A − 1 : H → V {\displaystyle A^{-1}:H\rightarrow V} is...

resolves the problem: Trace theorem — Assume Ω is bounded with Lipschitz boundary. Then there exists a bounded linear operator T : W 1 , p ( Ω ) → L p...

(\rho F_{i}),} where tr {\displaystyle \operatorname {tr} } is the trace operator. This is the POVM version of the Born rule. When the quantum state being...

singular trace is a trace on a space of linear operators of a separable Hilbert space that vanishes on operators of finite rank. Singular traces are a feature...

operator is a non-negative operator on a Hilbert space with unit trace. Mathematically, a quantum operation is a linear map Φ between spaces of trace...

In functional analysis, a branch of mathematics, a compact operator is a linear operator T : X → Y {\displaystyle T:X\to Y} , where X , Y {\displaystyle...

vectors comprising the basis. A density operator is a positive-semidefinite operator on the Hilbert space whose trace is equal to 1. For each measurement...