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searching for Trace operator 22 found (31 total)

Quadratic form (statistics) (969 words) [view diff] exact match in snippet view article

(\varepsilon ^{T}\Lambda \varepsilon )} . Next, by the cyclic property of the trace operator, E ⁡ [ tr ⁡ ( ε T Λ ε ) ] = E ⁡ [ tr ⁡ ( Λ ε ε T ) ] . {\displaystyle

Aharonov–Jones–Landau algorithm (2,506 words) [view diff] exact match in snippet view article find links to article

This is done by means of the Markov trace. The "Markov trace" is a trace operator defined on the Temperley–Lieb algebra T L n ( d ) {\displaystyle TL_{n}(d)}

Born rule (2,250 words) [view diff] exact match in snippet view article find links to article

(\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

Entropy (14,024 words) [view diff] exact match in snippet view article find links to article

{\rho }}} is a density matrix, t r {\displaystyle \mathrm {tr} } is a trace operator and ln {\displaystyle \ln } is a matrix logarithm. The density matrix

Trace (linear algebra) (5,480 words) [view diff] exact match in snippet view article

trace to arbitrary tensors. Gomme and Klein (2011) define a matrix trace operator trm {\displaystyle \operatorname {trm} } that operates on block matrices

Partial trace (2,121 words) [view diff] exact match in snippet view article find links to article

Hilbert spaces associated with quantum systems (see below). The partial trace operator can be defined invariantly (that is, without reference to a basis) as

POVM (3,082 words) [view diff] exact match in snippet view article find links to article

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

Block matrix (4,799 words) [view diff] exact match in snippet view article find links to article

\left(A^{\mathcal {B}}\right)_{ij}=B_{ji}} . As with the conventional trace operator, the block transpose is a linear mapping such that ( A + C ) B = A B

Chebyshev center (1,507 words) [view diff] exact match in snippet view article find links to article

where Tr ⁡ ( ⋅ ) {\displaystyle \operatorname {Tr} (\cdot )} is the trace operator and G = { ( Δ , x ) : f i ( Δ , x ) ≤ 0 , 0 ≤ i ≤ k , Δ = x x T } {\displaystyle

Characteristic function (probability theory) (5,208 words) [view diff] exact match in snippet view article

} where tr ⁡ ( ⋅ ) {\textstyle \operatorname {tr} (\cdot )} is the trace operator, If X is a complex random variable, then for t ∈ C φ X ( t ) = E ⁡ [

Itô's lemma (6,099 words) [view diff] exact match in snippet view article find links to article

f w.r.t. X, HX f is the Hessian matrix of f w.r.t. X, and Tr is the trace operator. We may also define functions on discontinuous stochastic processes

Determinant (13,785 words) [view diff] exact match in snippet view article find links to article

remaining polynomial is det(I + sA). For a positive definite matrix A, the trace operator gives the following tight lower and upper bounds on the log determinant

Measurement in quantum mechanics (8,320 words) [view diff] exact match in snippet view article find links to article

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

Vertex model (1,889 words) [view diff] exact match in snippet view article find links to article

{\displaystyle R(\lambda )^{-1}} and using the cyclic property of the trace operator that the following corollary holds. Corollary: For an integrable vertex

Multivariate Behrens–Fisher problem (1,770 words) [view diff] exact match in snippet view article find links to article

union-intersection principle Below, t r {\displaystyle \mathrm {tr} } indicates the trace operator. (as cited by ) T 2 ∼ ν p ν − p + 1 F p , ν − p + 1 , {\displaystyle

Quantum refereed game (3,254 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \operatorname {Tr} _{\mathcal {X}}(Z)} is the partial trace operator. The referee outputs a {\displaystyle a} with probability ⟨ A ⊗ B ,

Matrix calculus (7,065 words) [view diff] exact match in snippet view article find links to article

scalar-by-matrix derivatives (in the latter case, mostly involving the trace operator applied to matrices). In the latter case, the product rule can't quite

Gamma matrices (7,233 words) [view diff] exact match in snippet view article find links to article

Proving the above involves the use of three main properties of the trace operator: tr(A + B) = tr(A) + tr(B) tr(rA) = r tr(A) tr(ABC) = tr(CAB) = tr(BCA)

Harmonic map (5,239 words) [view diff] exact match in snippet view article find links to article

M an element of the tangent space Tf(p)N. By the definition of the trace operator, the laplacian may be written as ( Δ f ) p = ∑ i = 1 m ( ∇ ( d f ) )

Proofs involving ordinary least squares (5,246 words) [view diff] exact match in snippet view article find links to article

is equal to its own trace. This is useful because by properties of trace operator, tr(AB) = tr(BA), and we can use this to separate disturbance ε from

Acoustoelastic effect (6,219 words) [view diff] exact match in snippet view article find links to article

{\boldsymbol {E}}^{q}} where tr {\displaystyle \operatorname {tr} } is the trace operator, and q ∈ { 1 , 2 , 3 , … } {\displaystyle q\in \left\{1,2,3,\dots \right\}}

Adiabatic connection fluctuation dissipation theorem (2,292 words) [view diff] exact match in snippet view article find links to article

constant integration can then be carried out analytically. where the trace operator Tr ≡ ∬ d r d r ′ {\textstyle \operatorname {Tr} \equiv \iint drdr'}