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Boundary condition for generalized functions
In mathematical analysis, the trace operator extends the notion of the restriction of a function to the boundary of its domain to "generalized" functions
Trace_operator
Sum of elements on the main diagonal
size. Thus, similar matrices have the same trace. As a consequence, one can define the trace of a linear operator mapping a finite-dimensional vector space
Trace_(linear_algebra)
Compact operator for which a finite trace can be defined
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
Trace_class
Function over linear operators
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
Partial_trace
Concept in Hlibert spaces mathematics
matrices and linear operators on Hilbert spaces. This article covers some important operator inequalities connected with traces of matrices. Let H n
Trace_inequality
Mathematical concept
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
Weak_trace-class_operator
Topics referred to by the same term
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)
Trace
Topic in mathematics
it may be written as an integral operator of this form. The product of two Hilbert–Schmidt operators has finite trace-class norm; therefore, if A and B
Hilbert–Schmidt_operator
Property of a thermodynamic system
{\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
Entropy
Vector in statistics
(\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
Quadratic_form_(statistics)
Noncommutative geometric structure
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
Singular_trace
Extension of Lidskii's theorem
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
Grothendieck_trace_theorem
Quantum algorithm in computer science
Jones polynomial. 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
Aharonov–Jones–Landau algorithm
Aharonov–Jones–Landau_algorithm
Mathematical theorem
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
Selberg_trace_formula
Generalized measurement in quantum mechanics
(\rho F_{i})} , where tr {\displaystyle \operatorname {tr} } is the trace operator. When the quantum state being measured is a pure state | ψ ⟩ {\displaystyle
POVM
Norm on a vector space of matrices
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
Matrix_norm
Algebraic trace
trace, introduced by Jacques Dixmier (1966), is a non-normal trace on a space of linear operators on a Hilbert space larger than the space of trace class
Dixmier_trace
}}\gamma ({\vec {u}})=0\}} , where γ {\displaystyle \gamma } is the trace operator. Furthermore, A − 1 : H → V {\displaystyle A^{-1}:H\rightarrow V} is
Stokes_operator
p}(\partial M,N)} and that when N = R {\displaystyle N=\mathbb {R} } , the trace operator is onto. The proof of the surjectivity being based on an averaging argument
Sobolev_mapping
Calculation rule in quantum mechanics
(\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
Born_rule
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
Nuclear operators between Banach spaces
Nuclear_operators_between_Banach_spaces
Operator generalizing the Laplacian in differential geometry
In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space
Laplace–Beltrami_operator
In mathematics, a linear operator acting on inner product space
positive trace-class operators ρ {\displaystyle \rho } on H C {\displaystyle H_{\mathbb {C} }} for which Trace ρ = 1. {\displaystyle \mathop {\text{Trace}}
Positive_operator
Type of continuous linear operator
mathematics, a compact operator is a linear operator that behaves, in several important respects, like a finite-dimensional operator such as a matrix. In
Compact_operator
Vector space of functions in mathematics
theorem 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
Sobolev_space
different versions of the trace formula. The first version was the unrefined trace formula, whose terms depend on truncation operators and have the disadvantage
Arthur–Selberg_trace_formula
Mathematical tool in quantum physics
a positive semi-definite operator, see below. A density operator is a positive semi-definite, self-adjoint operator of trace one acting on the Hilbert
Density_matrix
Class of transformations that quantum systems and processes can undergo
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
Quantum_operation
Linear operator in mathematics
mathematics, the composition operator C ϕ {\displaystyle C_{\phi }} with symbol ϕ {\displaystyle \phi } is a linear operator defined by the rule C ϕ ( f
Composition_operator
*-algebra of bounded operators on a Hilbert space
bounded operators on a Hilbert space H is the Banach space of all trace class operators with the trace norm ||A||= Tr(|A|). The Banach space of trace class
Von_Neumann_algebra
Complex-valued function
operator. It is defined for bounded operators on a Hilbert space which differ from the identity operator by a trace-class operator (i.e. an operator whose
Fredholm_determinant
Identity in Itô calculus analogous to the chain rule
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
Itô's_lemma
In mathematics, invariant of square matrices
for particular kinds of operators. The Fredholm determinant defines the determinant for operators known as trace class operators by an appropriate generalization
Determinant
Mathematical conjecture about the Riemann zeta function
of number theory as a trace formula on noncommutative geometry of Adele classes. A possible connection of Hilbert–Pólya operator with quantum mechanics
Hilbert–Pólya_conjecture
Capability to trace something
force in 2002, making traceability compulsory for food and feed operators and requiring those businesses to implement traceability systems. The EU introduced
Traceability
Differential operator in mathematics
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean
Laplace_operator
Linear operator in functional analysis
{\displaystyle T} is then a compact operator, and one has the canonical form for compact operators. Compact operators are trace class only if the series ∑ i
Finite-rank_operator
Statistical term
{I} _{p})=p} , where Tr {\displaystyle \operatorname {Tr} } is the trace operator. Large leverage h i i {\displaystyle {h_{ii}}} corresponds to an x i
Leverage_(statistics)
differential operators". Mathematica Scandinavica. 2 (2): 267–285. doi:10.7146/math.scand.a-10414. JSTOR 24489040. Fichera, Gaetano (1965). "The trace operator. Sobolev
Ehrling's_lemma
Matrix defined using smaller matrices called blocks
\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
Block_matrix
Identifies the commutant of a specific von Neumann algebra
=1\otimes \delta _{1}} is a cyclic-separating trace vector. Moreover the modular conjugation operator J and commutant M ' can be explicitly identified
Commutation theorem for traces
Commutation_theorem_for_traces
operators on a Hilbert space H. B(H) admits a predual B*(H), the trace class operators on H. The ultraweak topology is the weak-* topology so induced;
Ultraweak_topology
Vector differential operator
Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by ∇ (the nabla
Del
Fourier transform of the probability density function
} 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 [
Characteristic function (probability theory)
Characteristic_function_(probability_theory)
Weak topology on function spaces
trace class operators C1(H), and it generates the w*-topology on B(H), called the weak-star operator topology or σ-weak topology. The weak-operator and
Weak_operator_topology
Quantum-mechanical simulation framework
constant integration can then be carried out analytically. where the trace operator Tr ≡ ∬ d r d r ′ {\textstyle \operatorname {Tr} \equiv \iint drdr'}
Adiabatic connection fluctuation dissipation theorem
Adiabatic_connection_fluctuation_dissipation_theorem
normal trace τ and the standard Gelfand–Naimark–Segal action of M on H = L2(M, τ), Edward Nelson proved that the measurable affiliated operators do form
Affiliated_operator
In operator theory, a Toeplitz operator is the compression of a multiplication operator on the circle to the Hardy space. Let S 1 {\displaystyle S^{1}}
Toeplitz_operator
Invariant in mathematics
a product of functions with different variables x1,..., xn, and the trace operator Tr means setting all the vectors xk equal. The zeroth transvectant is
Transvectant
Generators of the Clifford algebra for relativistic quantum mechanics
Proving the above involves the use of three main properties of the trace operator: tr ( A + B ) = tr ( A ) + tr ( B ) {\displaystyle \operatorname
Gamma_matrices
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
Chebyshev_center
Concept in quantum chemistry
the involved orbitals, and E m n {\displaystyle E_{mn}} operators are the spin-traced operators a m α † a n α + a m β † a n β {\displaystyle a_{m\alpha
Dyall_Hamiltonian
Bounded linear operator
… {\displaystyle k=0,1,2,\dots } . The operator norm of V is 2 / π {\displaystyle 2/\pi } . V is not trace class. V has no eigenvalues and therefore
Volterra_operator
Method for constructing existence proofs and calculating solutions in variational calculus
\mathbb {R} ^{m})} of functions whose trace is some fixed function g {\displaystyle g} in the image of the trace operator. This restriction allows finding
Direct method in the calculus of variations
Direct_method_in_the_calculus_of_variations
Construct in quantum information theory
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
Entanglement_witness
of Hilbert–Schmidt operators. British mathematician Nigel Kalton, noticing the spectral condition of Weiss, characterised all trace class commutators.
Commutator_subspace
Programming language feature
casting for why not Number trace(getQualifiedClassName(new Sprite())); // "flash.display.Sprite" Alternatively, the operator is can be used to determine
Type_introspection
Hilbert space of Hilbert–Schmidt operators. Moreover, the 1st Schatten class is the space of trace class operators. (Conway 2000, p. 93) Schatten, Robert
Schatten_class_operator
Elliptic differential operators in geometry mathematics
connection Laplacian is often called the Laplace–Beltrami operator. It is defined as the trace of the second covariant derivative: Δ T = tr ∇ 2 T , {\displaystyle
Laplace operators in differential geometry
Laplace_operators_in_differential_geometry
Approach used in computer vision systems
( μ ) − κ trace 2 ( μ ) . {\displaystyle H=\det(\mu )-\kappa \,\operatorname {trace} ^{2}(\mu ).} The determinant of the Hessian operator has been extended
Corner_detection
Interaction of a quantum system with a classical observer
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
Measurement in quantum mechanics
Measurement_in_quantum_mechanics
Foundational object in quantum communication theory
Terminologically, quantum channels are completely positive (CP) trace-preserving maps between spaces of operators. In other words, a quantum channel is just a quantum
Quantum_channel
1×1 matrix, such matrix 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
Proofs involving ordinary least squares
Proofs_involving_ordinary_least_squares
NASA satellite of the Explorer program
Transition Region and Coronal Explorer (TRACE, or Explorer 73, SMEX-4) was a NASA heliophysics and solar observatory designed to investigate the connections
TRACE
Mathematical norm
Hermitian operator | T | := ( T ∗ T ) {\displaystyle |T|:={\sqrt {(T^{*}T)}}} . The Schatten 1-norm is the nuclear norm (also known as the trace norm, or
Schatten_norm
{\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\}}
Acoustoelastic_effect
{\displaystyle R(\lambda )^{-1}} and using the cyclic property of the trace operator that the following corollary holds. Corollary: For an integrable vertex
Vertex_model
Specialized notation for multivariable calculus
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
Matrix_calculus
Concept in mathematics
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 ) )
Harmonic_map
operator denotes a type of expression that enters into an a-bar movement dependency. One often says that the operator "binds a variable". Operators are
Operator_(linguistics)
Markovian quantum master equation for density matrices (mixed states)
\{A_{m}\}} are arbitrary operators and h is a positive semidefinite matrix. The latter is a strict requirement to ensure the dynamics is trace-preserving and completely
Lindbladian
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
Multivariate Behrens–Fisher problem
Multivariate_Behrens–Fisher_problem
Number of vectors in any basis of the vector space
of a vector space may alternatively be characterized as the trace of the identity operator. For instance, tr id R 2 = tr ( 1 0 0 1 ) = 1 + 1 = 2
Dimension_(vector_space)
(on a complex Hilbert space) continuous linear operator
functional analysis, a normal operator on a complex Hilbert space H {\displaystyle H} is a continuous linear operator N : H → H {\displaystyle N\colon
Normal_operator
Term in quantum field theory
fermions, (−1)F is a unitary, Hermitian, involutive operator where F is the fermion number operator. For the example of particles in the Standard Model
(−1)F
{\displaystyle \operatorname {Tr} _{\mathcal {X}}(Z)} is the partial trace operator. The referee outputs a {\displaystyle a} with probability ⟨ A ⊗ B ,
Quantum_refereed_game
In physics, a linear operator acting on a vector space of linear operators
In physics, a superoperator is a linear operator acting on a vector space of linear operators. Sometimes the term refers more specially to a completely
Superoperator
Banach space of a dual
For 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
Predual
coroner's report. The coroner's office reports that the baby died of botulism traced to the baby food manufacturer's product. During a conference call, they
List_of_Traders_episodes
{\displaystyle \partial \Omega } . In general, if B {\displaystyle B} is any trace operator, one can construct the boundary value problem L u = f in Ω {\displaystyle
Elliptic boundary value problem
Elliptic_boundary_value_problem
Matrices similar to diagonal matrices
infinitesimal Hilbert–Schmidt operator. In fact, the above result could be further generalized: For any norm ideal that is not the trace class, with norm ‖ ⋅ ‖
Diagonalizable_matrix
Vector operator in vector calculus
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters
Divergence
Temporal logic
end) A trace satisfying this formula is given in the figure on the right. PSL's temporal operators can be roughly classified into LTL-style operators and
Property Specification Language
Property_Specification_Language
Mathematical compact operator
the trace on trace-class operators and det is the Fredholm determinant. For symmetrizable Hilbert–Schmidt operators the result states that the trace or
Symmetrizable compact operator
Symmetrizable_compact_operator
. In this space, every nuclear operator is of order zero, and is thus of trace-class. The idea of a nuclear operator can be adapted to Fréchet spaces
Fredholm_kernel
The zeta function of a mathematical operator O {\displaystyle {\mathcal {O}}} is a function defined as ζ O ( s ) = tr O − s {\displaystyle \zeta _{\mathcal
Zeta_function_(operator)
'analytic/global' side involves the usual trace on the Hilbert space and commutators of functions with the phase operator (which corresponds to the 'index' part
Spectral_triple
operators differ by a trace-class operator, then their absolutely continuous parts are unitarily equivalent. In particular if a self-adjoint operator
Weyl–von_Neumann_theorem
Hessian differential operator. Special cases include the Monge–Ampère equation and Poisson's equation (the Laplacian being the trace of the Hessian matrix)
Hessian_equation
Linear operator related to topological vector spaces
nuclear operators are an important class of linear operators introduced by Alexander Grothendieck in his doctoral dissertation. Nuclear operators are intimately
Nuclear_operator
Theorem
Radon–Nikodym theorem. The usual density operator of states on the matrix algebras with respect to the standard trace is nothing but the Radon–Nikodym derivative
Stinespring_dilation_theorem
Idempotent linear transformation from a vector space to itself
object. A projection on a vector space V {\displaystyle V} is a linear operator P : V → V {\displaystyle P\colon V\to V} such that P 2 = P {\displaystyle
Projection_(linear_algebra)
1934. They are closely related to operator concave and operator convex functions, and are encountered in operator theory and in matrix theory, and led
Operator_monotone_function
French mathematician
worked on operator algebras, especially C*-algebras, and wrote several of the standard reference books on them, and introduced the Dixmier trace and the
Jacques_Dixmier
Discrete analog of a derivative
differentiation. The difference operator, commonly denoted Δ {\displaystyle \Delta } (uppercase Delta), is the operator that maps a function f to the function
Finite_difference
Mathematical theorem
shows 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
Mercer's_theorem
Elliptic partial differential operator
p-Laplace operator, is a quasilinear elliptic partial differential operator of 2nd order. It is a nonlinear generalization of the Laplace operator, where
P-Laplacian
Hilbert–Carleman determinant is not multiplicative. If A {\displaystyle A} is a trace class operator, then the Hilbert–Carleman determinant is related to the Fredholm
Hilbert–Carleman_determinant
Sequence of steps used to access data in a SQL relational database management system
optimization include: SQL Trace Oracle Trace and TKPROF Microsoft SMS (SQL) Execution Plan Tableau Performance Recording (all DB) "SQL Trace". Microsoft.com. Microsoft
Query_plan
Mathematical problem in von Neumann algebra theory
of any (separable) von Neumann algebra is finitely representable in the trace class. In January 2020, Ji, Natarajan, Vidick, Wright, and Yuen announced
Connes_embedding_problem
TRACE OPERATOR
TRACE OPERATOR
Girl/Female
Greek American French
Reaper; from Therasia.
Female
English
Feminine variant spelling of English unisex Tracy, TRACIE means "place of Thracius."
Female
English
Feminine variant spelling of English unisex Tracy, TRACI means "place of Thracius."
Girl/Female
Greek American
Reap; from Therasia.
Girl/Female
American, Arabic, Australian, British, Chinese, Christian, Danish, English, French, German, Gujarati, Indian, Irish, Jamaican, Latin, Muslim, Portuguese, Swedish
Mercy; God's Favor; Grace; Grace of God; Kindness; Thanks; Love; Favour; Blessing; Charm; Good will
Surname or Lastname
English (Kent)
English (Kent) : perhaps a variant of Treece.Altered spelling of German Treis, a topographic name for someone who lived by or owned an uncultivated piece of land used as pasture, from Middle Low German drīsch ‘fallow land’, or a habitational name from a place named with this word (in Hessian dialect treis), in Hesse or on the Mosel river. Alternatively, in some instances it may be from a short form of the personal name Andreas (see Andrew).
Male
English
Variant spelling of English unisex Tracy, TRACEY means "place of Thracius."
Boy/Male
American, Anglo, Australian, British, Chinese, English, French
Fighter; Brave
Surname or Lastname
English
English : nickname from Middle English, Old French grace ‘charm’, ‘pleasantness’ (Latin gratia).English : from the female personal name Grace, which was popular in the Middle Ages. This seems in the first instance to have been from a Germanic element grīs ‘gray’ (see Grice 1), but was soon associated by folk etymology with the Latin word meaning ‘charm’.
Girl/Female
English American
from Thracia.
Girl/Female
English
from Thracia.
Surname or Lastname
English
English : probably from Middle English, Old French brace ‘arm’, also denoting a piece of armor covering the arm. In most cases it is probably a metonymic occupational name for a maker or seller of armor, specifically armor designed to protect the upper arms, but it could also have been a nickname for someone with strong arms (compare Armstrong) or a deformed or otherwise noticeable arm.
Girl/Female
Latin American English Irish
Grace.
Male
English
English surname transferred to unisex forename use, from a Norman baronial name TRACY means "place of Thracius."
Boy/Male
Anglo Saxon American Greek
Brave.
Male
English
Short form of English unisex Tracy, TRACE means "place of Thracius."
Surname or Lastname
English
English : perhaps a variant of Treece.
Boy/Male
Anglo Saxon American Latin Greek English French
Brave.
Boy/Male
Anglo Saxon American English French
Brave.
Female
English
Feminine variant spelling of English unisex Tracy, TRACEE means "place of Thracius."
TRACE OPERATOR
TRACE OPERATOR
Girl/Female
Hindu, Indian, Traditional
Shiva
Male
Portuguese
Portuguese form of Latin Salomon, SALOMÃO means "peaceable."
Boy/Male
Hindu, Indian
In Harmony
Boy/Male
Tamil
Lord Vishnu
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Lord Shiva
Boy/Male
Hindu, Indian, Marathi, Oriya, Telugu, Traditional
Fortunate
Male
French
French form of Teutonic Ermingild, ERMENEGILDE means "all-giving."Â
Boy/Male
Muslim/Islamic
st month of Islamic year
Boy/Male
Tamil
Khileshwar | கீலேஷà¯à®µà®°Â
Supreme being
Girl/Female
Hindu, Indian
Goddess Durga
TRACE OPERATOR
TRACE OPERATOR
TRACE OPERATOR
TRACE OPERATOR
TRACE OPERATOR
v. t.
To run a race with.
v.
The trade winds.
v.
Continuity or extension of anything; as, the tract of speech.
n.
A tract or area, as of land.
v.
A company of men engaged in the same occupation; thus, booksellers and publishers speak of the customs of the trade, and are collectively designated as the trade.
v.
Track; trace.
v. t.
To mark out; to draw or delineate with marks; especially, to copy, as a drawing or engraving, by following the lines and marking them on a sheet superimposed, through which they appear; as, to trace a figure or an outline; a traced drawing.
n.
One who, or that which, traces.
v. t.
To add grace notes, cadenzas, etc., to.
v. t.
To trace out; to track; also, to draw out; to protact.
n.
Course; way; as, the track of a comet.
v. t.
To follow the tracks or traces of; to pursue by following the marks of the feet; to trace; to trail; as, to track a deer in the snow.
v. t.
A mark left by anything passing; a track; a path; a course; a footprint; a vestige; as, the trace of a carriage or sled; the trace of a deer; a sinuous trace.
v. t.
To supply with heavenly grace.
v. t.
To trace by scent; to track; -- a hunting term.
v. t.
To cause to contend in a race; to drive at high speed; as, to race horses.
v. t.
Hence, to follow the trace or track of.
n.
A mark left by something that has passed along; as, the track, or wake, of a ship; the track of a meteor; the track of a sled or a wheel.
n.
A mark or impression left by the foot, either of man or beast; trace; vestige; footprint.
imp. & p. p.
of Trace