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Compact operator for which a finite trace can be defined
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
Trace_class
Sum of elements on the main diagonal
This trace can be generalized to von Neumann Algebras. The Dixmier trace generalizes the usual trace beyond trace-class operators. The partial trace is
Trace_(linear_algebra)
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
Function over linear operators
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
Partial_trace
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
Nuclear operators between Banach spaces
Nuclear_operators_between_Banach_spaces
Report of stack frames during program execution
In computing, a stack trace (also called stack backtrace or stack traceback) is a report of the active stack frames at a certain point in time during
Stack_trace
Complex-valued function
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)
Fredholm_determinant
Noncommutative geometric structure
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
Singular_trace
Matrices similar to diagonal matrices
(|T|^{p})^{1/p}} , where Tr {\displaystyle \operatorname {Tr} } is the trace. The p-Schatten class is the set of all operators with finite p-Schatten norm. Weyl
Diagonalizable_matrix
Type of continuous linear operator
\sum _{n}s_{n}^{2}<\infty ,} and trace class when ∑ n s n < ∞ . {\displaystyle \sum _{n}s_{n}<\infty .} Every trace-class operator is Hilbert–Schmidt, and
Compact_operator
Mathematical norm
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
Schatten_norm
In mathematics, the Arthur–Selberg trace formula is a generalization of the Selberg trace formula from the group SL2 to arbitrary reductive groups over
Arthur–Selberg_trace_formula
Algebraic trace
than the space of trace class operators. Dixmier traces are examples of singular traces. Some applications of Dixmier traces to noncommutative geometry
Dixmier_trace
Topic in mathematics
of this form. 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
Hilbert–Schmidt_operator
Concept in Hlibert spaces mathematics
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
Trace_inequality
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
Generalization of finite-dimensional Euclidean spaces different from Hilbert spaces
Hilbert spaces and trace class operators, which are easier to understand. (On Hilbert spaces nuclear operators are often called trace class operators.) We
Nuclear_space
Class of transformations that quantum systems and processes can undergo
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
Quantum_operation
is also true if the Hilbert–Schmidt class is replaced by any Schatten class Sp with p ≠ 1. For S1, the trace-class operators, the situation is quite different
Weyl–von_Neumann_theorem
American actress (born 1981)
Trace Lysette (born 1981) is an American actress whose most notable roles include Shea in the television series Transparent (2014–2019) and Tracey in
Trace_Lysette
Expected value of a quantum measurement
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
Expectation value (quantum mechanics)
Expectation_value_(quantum_mechanics)
Generalization of strings in computer science
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
Trace_monoid
Mathematical theorem
In mathematics, the Selberg trace formula, introduced by Selberg (1956), is an expression for the character of the unitary representation of a Lie group
Selberg_trace_formula
Identifies the commutant of a specific von Neumann algebra
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
Commutation theorem for traces
Commutation_theorem_for_traces
Element of low concentration
micronutrients. The two types of trace element in biochemistry are classed as essential or non-essential. An essential trace element is a dietary element
Trace_element
For two suitable matrices, A and B, I+AB and I+BA have the same determinant
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)
Weinstein–Aronszajn_identity
Kalton, noticing the spectral condition of Weiss, characterised all trace class commutators. Kalton's result forms the basis for the modern characterisation
Commutator_subspace
Number of vectors in any basis of the vector space
"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
Dimension_(vector_space)
Mathematical problem in von Neumann algebra theory
any (separable) von Neumann algebra is finitely representable in the trace class. In January 2020, Ji, Natarajan, Vidick, Wright, and Yuen announced a
Connes_embedding_problem
2nd Schatten class is in fact the Hilbert space of Hilbert–Schmidt operators. Moreover, the 1st Schatten class is the space of trace class operators. (Conway
Schatten_class_operator
Weak topology on function spaces
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
Weak_operator_topology
Linear operator in mathematics
questions include whether C ϕ {\displaystyle C_{\phi }} is compact or trace-class; answers typically depend on how the function φ {\displaystyle \varphi
Composition_operator
Physics phenomenon
positive-semidefinite matrix, or a trace class when the state space is infinite-dimensional, and which has trace 1. By the spectral theorem, such a matrix
Quantum_entanglement
Linear operator in functional analysis
has the canonical form for compact operators. Compact operators are trace class only if the series ∑ i α i {\textstyle \sum _{i}\alpha _{i}} is convergent;
Finite-rank_operator
Theorem
Construction for adding objects to a Hilbert space Trace class – Compact operator for which a finite trace can be defined Schaefer & Wolff 1999, p. 172. Grothendieck
Schwartz_kernel_theorem
Banach space of a dual
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
Predual
Mathematical function
In mathematics, the field trace is a particular function defined with respect to a finite field extension L/K, which is a K-linear map from L onto K.
Field_trace
Mathematical theorem
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
Extension of Lidskii's theorem
analysis, the Grothendieck trace theorem is an extension of Lidskii's theorem about the trace and the determinant of a certain class of nuclear operators on
Grothendieck_trace_theorem
Bounded linear operator
. The operator norm of V is 2 / π {\displaystyle 2/\pi } . V is not trace class. V has no eigenvalues and therefore, by the spectral theory of compact
Volterra_operator
Class of Turkish patrol vessels
The Hisar-class offshore patrol vessels are patrol vessels / corvette that will allow the Turkish Navy to perform cost-effective patrol missions. They
Hisar-class offshore patrol vessel
Hisar-class_offshore_patrol_vessel
'geometric/local' side involves the Dixmier trace and commutators with the Dirac operator (which corresponds to the 'characteristic class integration' part of the index
Spectral_triple
Generalization of the concept from statistical mechanics
infinite-dimensional, then, for the above notation to be valid, the argument must be trace class, that is, of a form such that the summation exists and is bounded. The
Partition function (mathematics)
Partition_function_(mathematics)
bounded 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
Public, coeducational high school in Washington Court House, Ohio, United States
graduated from Miami Trace, a proven rate of success for its students. Within the 61st graduating class at Miami Trace, the class of 2023, a wide variety
Miami_Trace_High_School
Amine receptors in the mammalian brain
Trace amines are an endogenous group of trace amine-associated receptor 1 (TAAR1) agonists – and hence, monoaminergic neuromodulators – that are structurally
Trace_amine
German mathematician (born 1949)
233–305. doi:10.1016/0001-8708(78)90116-0. Muller, Werner (1989). "The trace class conjecture in the theory of automorphic forms". Annals of Mathematics
Werner_Müller_(mathematician)
Type of state in thermal systems
phase transitions, spontaneous symmetry breaking, operators that are not trace class, divergent partition functions, etc.. The complex functions of z, ⟨ α
KMS_state
Physics of many interacting particles
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
Statistical_mechanics
*-algebra of 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 operators is itself the dual of
Von_Neumann_algebra
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
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
} of the predual L ∗ ( H ) {\displaystyle L_{*}(H)} that consists of trace class operators. It was introduced by John von Neumann in 1936. The ultrastrong
Ultrastrong_topology
EDA/CAD software for creating schematic diagrams and printed circuit boards
DipTrace is a proprietary software suite for electronic design automation (EDA) used for electronic schematic capture and printed circuit board layouts
DipTrace
Country in South Asia
Kathakali, Kuchipudi, Manipuri, Mohiniattam, Odissi, Sattriya, and Yakshagana) trace their roots to religious practices (...) the Indian diaspora has led to
India
Systems for grouping fossilised evidence of biological activity
Trace fossils are classified in various ways for different purposes. Traces can be classified taxonomically (by morphology), ethologically (by behavior)
Trace_fossil_classification
In mathematics, invariant of square matrices
Fredholm determinant defines the determinant for operators known as trace class operators by an appropriate generalization of the formula det ( I + A
Determinant
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. A nuclear
Fredholm_kernel
British television channel
Trace Vault (formerly Video Vault and The Vault) was a British free-to-air music and entertainment television channel owned by Trace Group. On 1 November
Trace_Vault
Season of television series
The sixth season of Without a Trace began airing in United States on September 27, 2007. Twelve episodes had been completed before the WGA Strike. A further
Without_a_Trace_season_6
Polish mathematician (born 1956)
806. with Ken Dykema, Gary Weiss: Unitarily invariant trace extensions beyond the trace class. In: Complex analysis and related topics (Cuernavaca, 1996)
Mariusz_Wodzicki
TRACE is a connectionist model of speech perception, proposed by James McClelland and Jeffrey Elman in 1986. It is based on a structure called "the TRACE"
TRACE_(psycholinguistics)
{\displaystyle a_{1},\dots ,a_{n}\in \mathbb {R} } and K {\displaystyle K} is a trace class operator called the extended Brownian scattering operator and the subscript
KPZ_fixed_point
representation theorem Rigged Hilbert space Spectral theorem, Spectral theory Trace class Normed vector space Unit ball Banach space Hahn–Banach theorem Dual space
List of functional analysis topics
List_of_functional_analysis_topics
Defunct American defense electronics contractor
Tracor, Inc. was a major North American defense electronics contractor which was acquired by Marconi Electronic Systems (MES), a subsidiary of General
Tracor
Linear operator related to topological vector spaces
product constructions for topological vector spaces Trace class – Compact operator for which a finite trace can be defined Topological vector space – Vector
Nuclear_operator
{\displaystyle f^{1/2}K_{\operatorname {Ai} }^{\operatorname {ext} }f^{1/2}} is a trace class operator on L 2 ( { t 1 , … , t n } × R ) {\displaystyle L^{2}(\{t_{1}
Airy_process
Class of American littoral combat ships
The Freedom-class is one of two classes of the littoral combat ship program built for the United States Navy. The Freedom-class was proposed by a consortium
Freedom-class littoral combat ship
Freedom-class_littoral_combat_ship
) π ( x ) d x {\displaystyle \pi (f)=\int _{G}f(x)\pi (x)\,dx} is of trace class, and the distribution Θ π : f ↦ Tr ( π ( f ) ) {\displaystyle \Theta
Harish-Chandra_character
1847 novel by Emily Brontë
Heights for 60 years who is a rigid, self-righteous Christian but lacks any trace of genuine kindness or humanity. He hates nearly everyone in the novel except
Wuthering_Heights
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
Application layer protocol
specification added five new methods: PUT, DELETE, CONNECT, OPTIONS, and TRACE. Any client can use any method and the server can be configured to support
HTTP
Topologies on operators on a Hilbert space
(unique) predual B ( H ) ∗ {\displaystyle B(H)_{*}} , consisting of the trace class operators, whose dual is B(X). The seminorm pw(x) for w positive in the
Operator_topologies
Crime fiction novel by Patricia Cornwell
Trace is a 2004 crime fiction novel by Patricia Cornwell. It is the thirteenth book of the Dr. Kay Scarpetta series. Dr. Kay Scarpetta, having left Richmond
Trace_(novel)
Mathematical structures that allow quantum mechanics to be explained
mixed state is a trace class, nonnegative (positive semi-definite) self-adjoint operator ρ {\displaystyle \rho } normalized to be of trace 1. In turn, any
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Quantum states that are not entangled
matrices are replaced by positive trace class operators with trace 1, and a state is separable if it can be approximated, in trace norm, by states of the above
Separable_state
American mathematician
Journal of Mathematics, 24(2), 216. Johnson, D. L.; Lahr, C. D. The trace class of an arbitrary Hilbert algebra. Comment. Math. Univ. St. Paul. 28 (1980)
Charles_Dwight_Lahr
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
Lp, p ≥ 1, correspond to the lp sequence spaces. In particular, the trace class operators correspond to l1 and the Hilbert-Schmidt operators correspond
Calkin_correspondence
Statistical mechanics of quantum-mechanical systems
E_{n}} of H go to +∞ sufficiently fast, e−r H will be a non-negative trace-class operator for every positive r. The canonical ensemble (or sometimes Gibbs
Quantum_statistical_mechanics
Theory of logic to account for observations from quantum theory
Then for any quantum probability measure P on Q there exists a unique trace class operator S such that P ( E ) = Tr ( S E ) {\displaystyle \operatorname
Quantum_logic
In mathematics, the trace field of a linear group is the field generated by the traces of its elements. It is mostly studied for Kleinian and Fuchsian
Trace field of a representation
Trace_field_of_a_representation
Frigate class of the Turkish Naval Forces
The Istanbul-class frigates (also known as TF-100, MILGEM II, İstif and I class) are a class of multirole frigates currently being constructed for the
Istanbul-class_frigate
Kingdom of life
Australia. These fossils are interpreted as most probably being early sponges. Trace fossils such as tracks and burrows found in the Tonian period (from 1 gya)
Animal
Programming language feature
getQualifiedClassName; import flash.display.Sprite; // trace is like System.out.println() in Java or echo in PHP trace(getQualifiedClassName("I'm a String"));
Type_introspection
Type of lawsuit
sue under Section 11 of the 1933 Act in a class action, a plaintiff must be able to prove that he can trace his shares to the registration statement in
Class_action
Trace fossil
Isopodichnus is an ichnogenus of trace fossil. Ribbon-like in form, Isopodichnus traces were likely formed by the activity of an isopod crustacean foraging
Isopodichnus
German executive car
programme that allocated all of its products into Classes, the product line of the mid-range cars traces decades before. Officially Mercedes-Benz recognising
Mercedes-Benz_E-Class
Produce traceability makes it possible to track produce from its point of origin to a retail location where it is purchased by consumers. Produce traceability
Produce_traceability
Puerto Rican actress and dancer (born 1973)
known for her roles as Elena Delgado on the CBS police procedural Without a Trace (2005–2009), as Carmen Luna on the Lifetime comedy-drama Devious Maids (2013–2016)
Roselyn_Sánchez
American television sitcom (2010–2014)
when she was sixteen. Virginia works as a maid, cleaning houses of upper-class people while the Chances appear to live just above the poverty line. Garret
Raising_Hope
Cryptographic methods built using trace zero varieties from algebraic geometry
Frey in 1998, trace zero cryptography refers to the use of trace zero varieties (TZV) for cryptographic purpose.[citation needed] Trace zero varieties
Trace_zero_cryptography
Trace fossil
Tektonargus is a trace fossil ichnotaxon genus of insect, from the Late Jurassic period. It was discovered in a section of the Morrison Formation, located
Tektonargus
Locally convex topological vector space
{\displaystyle H} is infinite, then S 1 ( H ) {\displaystyle S_{1}(H)} (the trace class) is not reflexive, because it contains a subspace isomorphic to ℓ 1
Reflexive_space
Spanish Navy submarine class
The S-80 Plus class (or Isaac Peral class) is a Spanish class of four submarines being built by the state-owned Spanish company Navantia at its Cartagena
S-80_Plus-class_submarine
Early modern fortification style built to withstand cannon fire
A bastion fort or trace italienne (a phrase derived from non-standard French, meaning 'Italian outline') is a fortification in a style developed during
Bastion_fort
Class of G protein-coupled receptors
Trace amine-associated receptors (TAARs), sometimes referred to as trace amine receptors (TAs or TARs), are a class of G protein-coupled receptors that
Trace amine-associated receptor
Trace_amine-associated_receptor
Model of computation
sense of use, the class naturally contains all of BPP, and the power of the class is focused on the "inherently quantum" power. Trace estimation is complete
One_clean_qubit
Debugging interface for embedded systems
half duplex only and bandwidth is limited. Trace is not supported. Class 2 adds ownership trace and program trace and allows the auxiliary debugging port
Nexus_(standard)
TRACE CLASS
TRACE CLASS
Male
English
English surname transferred to unisex forename use, from a Norman baronial name TRACY means "place of Thracius."
Girl/Female
English American
from Thracia.
Girl/Female
Latin American English Irish
Grace.
Boy/Male
American, Anglo, Australian, British, Chinese, English, French
Fighter; Brave
Female
English
Feminine variant spelling of English unisex Tracy, TRACI means "place of Thracius."
Surname or Lastname
English
English : perhaps a variant of Treece.
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’.
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 : 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.
Boy/Male
Anglo Saxon American Greek
Brave.
Boy/Male
Anglo Saxon American English French
Brave.
Male
English
Variant spelling of English unisex Tracy, TRACEY means "place of Thracius."
Female
English
Feminine variant spelling of English unisex Tracy, TRACEE means "place of Thracius."
Girl/Female
Greek American French
Reaper; from Therasia.
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).
Boy/Male
Anglo Saxon American Latin Greek English French
Brave.
Female
English
Feminine variant spelling of English unisex Tracy, TRACIE means "place of Thracius."
Male
English
Short form of English unisex Tracy, TRACE means "place of Thracius."
Girl/Female
Greek American
Reap; from Therasia.
TRACE CLASS
TRACE CLASS
Male
Native American
Native American Shawnee name CATAHECASSA means "black hoof."
Boy/Male
Bengali, Indian
The Vedas of the Moon
Girl/Female
Indian
The Sun, Lord Shiva
Female
English
Feminine form of English unisex Garnet, GARNETTE means "garnet (the gem)."
Male
Russian
(Ðазар) Russian form of Latin Nazarius, NAZAR means "of Nazareth." Compare with another form of Nazar.
Boy/Male
Indian, Punjabi, Sikh
Godlike Person
Girl/Female
English
Unity; concord; musically in tune. Harmonia was the mythological daughter of Aphrodite.
Boy/Male
Hindu, Indian
New; Novel
Girl/Female
Indian, Telugu
Softened
Girl/Female
Hindu, Indian
Lovely; Love to Life
TRACE CLASS
TRACE CLASS
TRACE CLASS
TRACE CLASS
TRACE CLASS
n.
Course; way; as, the track of a comet.
v. t.
To trace by scent; to track; -- a hunting term.
v.
The trade winds.
imp. & p. p.
of Trace
v. t.
To run a race with.
n.
A mark or impression left by the foot, either of man or beast; trace; vestige; footprint.
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 add grace notes, cadenzas, etc., to.
n.
One who, or that which, traces.
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.
Hence, to follow the trace or track of.
v.
Continuity or extension of anything; as, the tract of speech.
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 trace out; to track; also, to draw out; to protact.
v. t.
To cause to contend in a race; to drive at high speed; as, to race horses.
v.
Track; trace.
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.
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.
A tract or area, as of land.