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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
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
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)
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
}}\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
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
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
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)
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
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
*-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
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
Country in Southeast Asia
destinations to visit. Much of Vietnam's modern transportation network can trace its roots to the French colonial era, when it was used to facilitate the
Vietnam
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
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
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
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
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
1990–1991 conflict in the Middle East
confidence that sarin is a causative agent of GWI. Elizabeth Neuffer Iraqis Trace Surge in Cancer to US Bombings Archived 2 September 2013 at the Wayback
Gulf_War
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
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
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
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
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
Islamist terrorist attack in Indian-administered Kashmir
Hindu tourists, though a Christian tourist and a local Muslim pony ride operator were also killed. The attackers, armed with M4 carbines and AK-47s, entered
2025_Pahalgam_attack
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)
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
Twin-aisle airliner family
longer-range variant, followed in 1998 with Canada 3000 as the launch operator. The A330 shares many underpinnings with the airframe of the early A340
Airbus_A330
Political ideology promoting free-market capitalism
occurred during the 1970s energy crisis; he and sociologist Thomas Volscho trace the origin of its political rise to Lewis Powell's 1971 confidential memorandum
Neoliberalism
U.S. territory in the Caribbean
born in the 50 U.S. states, the District of Columbia or elsewhere, but trace their family ancestry to Puerto Rico. "Catholic Church and Puerto Rico officials
Puerto_Rico
Free and open-source anonymity network based on onion routing
technique is called onion routing. Using Tor makes it more difficult to trace a user's internet activity by preventing any single point on the internet
Tor_(network)
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
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
Country in Southern and Western Europe
and many prevailing forms, such as the symphony, concerto, and sonata, trace their roots back to innovations in 16th- and 17th-century Italian music
Italy
NASA/ESA space telescope launched in 1990
Earth orbit by a rocket. The history of the Hubble Space Telescope can be traced to 1946, to astronomer Lyman Spitzer's paper "Astronomical advantages of
Hubble_Space_Telescope
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
1959 American plane crash
in his flight plan, Dwyer became concerned. At his request, the radio operator tried to contact Peterson, to no response. The Bonanza had impacted the
The_Day_the_Music_Died
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
State in western India
during their koli dance performances. Modern Theatre in Maharashtra can trace its origins to the British colonial era in the middle of the 19th century
Maharashtra
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)
Military advanced trainer aircraft by Northrop
first supersonic trainer as well as the most produced. The T-38 can be traced back to 1952 and Northrop's N-102 Fang and N-156 fighter aircraft projects
Northrop_T-38_Talon
Iranian unmanned aerial combat vehicles
Retrieved 28 November 2025. Anwer, Ammar (8 November 2025). "Malawi moves to trace girls forced into Russian drone production". TVP World. Archived from the
Shahed_drones
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
American singer and actress (born 1946)
original on August 23, 2017. Retrieved March 2, 2025. King, Tom (2000). The Operator: David Geffen Builds, Buys, and Sells the New Hollywood. Random House.
Cher
1921 mass violence in Oklahoma, US
shoeshiner, was accused of assaulting Sarah Page, a white 21-year-old elevator operator in the nearby Drexel Building. He was arrested and rumors spread that he
Tulsa_race_massacre
2022 mass shooting in Texas, U.S.
Archived from the original on May 26, 2022. Retrieved May 26, 2022. Cohen, Trace William (May 26, 2022). "Texas Shooting Gunman Entered School 'Unobstructed'
Uvalde_school_shooting
French footballer (born 1987)
with the Korean automobile manufacturer Hyundai, the French telephone operator SFR and its subsidiary BuzzMobile, the French bank LCL and the sports betting
Karim_Benzema
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
Operating system for mobile devices
over, Android previously used Dalvik as a process virtual machine with trace-based just-in-time (JIT) compilation to run Dalvik "dex-code" (Dalvik Executable)
Android_(operating_system)
Principle in quantum information theory
mathematically by comparing the trace of σ and the trace of P(σ), with the trace being taken over the subspace HA. Since the trace is only over a subspace, it
No-communication_theorem
Term in quantum mechanics
absolute value of an operator is here defined as | A | ≡ A † A {\displaystyle |A|\equiv {\sqrt {A^{\dagger }A}}} . Since the trace of a matrix is equal
Fidelity_of_quantum_states
2014 American TV series or program
babysitting a neighbors' children, then the violent intruder vanishes without a trace, and the case goes cold till police links the case to Duane Owen. 29 3 "Midlife
Your_Worst_Nightmare
Programming language for statistics
of the command-line interface. In R, the generally preferred assignment operator is an arrow made from two characters <-, although = can be used in some
R_(programming_language)
Special forces unit of the British Army
operational control of the Director Special Forces. The Special Air Service traces its origins to 1941 during the Second World War. It was reformed as part
Special_Air_Service
Country in East Africa
were paved and as of 2012[update] private bus companies were the main operators of buses on the international route to Kigali; however, there were no
Burundi
Naval infantry branch of the U.S. military
highest-priority challenges." The move leaves the Army as the sole American operator of tanks. The organic aviation capability of the Marine Corps is essential
United_States_Marine_Corps
Non-commercial use of the radio spectrum
least every ten minutes and at the end of the conversation. Amateur radio operators must hold an amateur radio licence, granted after an examination that
Amateur_radio
Mythical creature
misidentification, and hoax, and the creature is not a real living animal. Folklorists trace the phenomenon of Bigfoot to a combination of factors and sources, including
Bigfoot
Barrier that stops or restricts the flow of surface or underground streams
downstream nations. The English word dam is found in Middle English, and traces back to dam in the Germanic languages Middle Low German, Middle Dutch, and
Dam
Armored personnel carrier
variant. K216: NBC reconnaissance vehicle. Equipped with detection system to trace sources of NBC agents. K221: Smoke generating vehicle. Produces two types
K200_KIFV
Force in Lebanon to withdraw from the country. U.S. intelligence later traced the financing and logistics of the attack to the Iranian embassy in Damascus
List of extrajudicial killings and political violence in Lebanon
List_of_extrajudicial_killings_and_political_violence_in_Lebanon
American singer and songwriter (born 1958)
after graduation. Jackson worked as a construction worker and forklift operator while playing in small clubs across Georgia. When he was 27, Jackson and
Alan_Jackson
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
was appointed for Trace, and he sued Mr. Cogan and the other former directors of Trace. His theory was that Mr. Cogan had treated Trace as a personal holding
Marshall_Cogan
Ukrainian 155 mm self-propelled howitzer
crossed. According to Roblin, the development of the Bohdana, which could be traced back to a proposed truck-mounted design back in 2009, would only begin in
2S22_Bohdana
Rimless, centerfire, bottlenecked rifle cartridge
least 13 metres (14 yd) a minimum 750 metres (820 yd) long red coloured trace. Produced by General Dynamics Ordnance and Tactical Systems – Canada. C24
7.62×51mm_NATO
Provincial capital of Quebec, Canada
long-distance bus network, is adjacent to the train station, and is used by operators such as Orleans Express and Intercar. Quebec City is served by Jean Lesage
Quebec_City
American multinational financial technology company
in the United States. In January 2021, PayPal became the first foreign operator with 100% control of a payment platform in China, gaining an advanced position
PayPal
Matrix whose only nonzero elements are on its main diagonal
&a_{n}\end{bmatrix}}^{\textsf {T}}} using the diag {\displaystyle \operatorname {diag} } operator: D = diag ( a 1 , … , a n ) . {\displaystyle \mathbf {D} =\operatorname
Diagonal_matrix
American actor (born 1930)
Detroit, to Thelma Hazel Alvera (née Boe; 1898–1993), a former telephone operator, and Robert John Wagner Sr. (1890–1964), a traveling salesman who worked
Robert_Wagner
Mathematical transform that expresses a function of time as a function of frequency
{\displaystyle {\mathcal {F}}[\psi ]=e^{-itN}\psi .} The operator N {\displaystyle N} is the number operator of the quantum harmonic oscillator written as N ≡
Fourier_transform
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
Emergency number in several countries
trace both landline and mobile telephone numbers with the BT operator; the former can be traced to an address. The latter can be immediately traced to
999 (emergency telephone number)
999_(emergency_telephone_number)
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
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
French jet fighter aircraft
started, which became the basis of multiple export variants. The largest operator of the type is the French Air and Space Force, followed by the United Arab
Dassault_Mirage_2000
Online subculture
supported pedophilia. The report also exposed that the incel forum site operators had changed a forum rule in March 2022, to allow for the sexualization
Incel
Second crewed mission to orbit the Moon
States' Apollo program and the second to orbit the Moon. NASA, the mission's operator, described it as a "dress rehearsal" for the first Moon landing (Apollo
Apollo_10
History of the commercial TV and radio network
were produced by Jerry Bruckheimer. These included Cold Case, Without a Trace, Criminal Minds, NCIS, and The Mentalist, along with CSI spinoffs CSI: Miami
History_of_CBS
of Hilbert–Schmidt operators. British mathematician Nigel Kalton, noticing the spectral condition of Weiss, characterised all trace class commutators.
Commutator_subspace
TRACE OPERATOR
TRACE OPERATOR
Female
English
Feminine variant spelling of English unisex Tracy, TRACI means "place of Thracius."
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).
Girl/Female
Greek American French
Reaper; from Therasia.
Boy/Male
Anglo Saxon American English French
Brave.
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
English : perhaps a variant of Treece.
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
English American
from Thracia.
Male
English
Short form of English unisex Tracy, TRACE means "place of Thracius."
Girl/Female
Latin American English Irish
Grace.
Boy/Male
Anglo Saxon American Greek
Brave.
Male
English
English surname transferred to unisex forename use, from a Norman baronial name TRACY means "place of Thracius."
Boy/Male
Anglo Saxon American Latin Greek English French
Brave.
Male
English
Variant spelling of English unisex Tracy, TRACEY means "place of Thracius."
Girl/Female
English
from Thracia.
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’.
Female
English
Feminine variant spelling of English unisex Tracy, TRACEE means "place of Thracius."
Girl/Female
Greek American
Reap; from Therasia.
Boy/Male
American, Anglo, Australian, British, Chinese, English, French
Fighter; Brave
Female
English
Feminine variant spelling of English unisex Tracy, TRACIE means "place of Thracius."
TRACE OPERATOR
TRACE OPERATOR
Girl/Female
Arabic, Australian
Cute Girl; Soft Lion
Girl/Female
American, Australian, British, Christian, English, French, German, Greek, Latin
Maiden; Coral; Nature Name; Small Pebble
Male
Babylonian
, the father of the demiurgus Bel.
Boy/Male
Muslim
Sparkle of light, Fire
Girl/Female
Muslim
A narrator of Hadith
Girl/Female
French American
Rules her household. Feminine of Harry from Henry.
Boy/Male
Egyptian Hindi
Born second.
Boy/Male
Greek Spanish
Friendly.
Boy/Male
Hindu, Indian
Blooming; Jupiter
Girl/Female
Indian
Goddess of will, Companion
TRACE OPERATOR
TRACE OPERATOR
TRACE OPERATOR
TRACE OPERATOR
TRACE OPERATOR
n.
One who, or that which, traces.
v. t.
To trace out; to track; also, to draw out; to protact.
n.
A tract or area, as of land.
v. t.
Hence, to follow the trace or track of.
n.
A mark or impression left by the foot, either of man or beast; trace; vestige; footprint.
v.
Continuity or extension of anything; as, the tract of speech.
v. t.
To add grace notes, cadenzas, etc., to.
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 trace by scent; to track; -- a hunting term.
imp. & p. p.
of Trace
v. t.
To run a race with.
n.
Course; way; as, the track of a comet.
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.
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.
Track; trace.
v. t.
To cause to contend in a race; to drive at high speed; as, to race horses.
v.
The trade winds.
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.
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. t.
To supply with heavenly grace.