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Noncommutative geometric structure
a 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
Singular_trace
Sum of elements on the main diagonal
source needed] Trace of a tensor with respect to a metric tensor Characteristic function Field trace Golden–Thompson inequality Singular trace Specht's theorem
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
Norm on a vector space of matrices
singular values of A {\displaystyle A} . The second equality is proven by explicit computation of t r a c e ( A ∗ A ) {\displaystyle \mathrm {trace}
Matrix_norm
Square roots of the eigenvalues of the self-adjoint operator
using singular values. For example, the Ky Fan k {\displaystyle k} -norm is the sum of first k {\displaystyle k} singular values, the trace norm is
Singular_value
Matrix decomposition
the largest singular value of M . {\displaystyle \mathbf {M} .} The last of the Ky Fan norms, the sum of all singular values, is the trace norm (also
Singular_value_decomposition
Algebraic trace
space of trace class operators. Dixmier traces are examples of singular traces. Some applications of Dixmier traces to noncommutative geometry are described
Dixmier_trace
Hypothetical event
The technological singularity, often simply called the singularity, is a hypothetical event in which technological growth accelerates beyond human control
Technological_singularity
Hypothetical phenomenon
In general relativity, a naked singularity is a hypothetical gravitational singularity without an event horizon. When there exists at least one causal
Naked_singularity
2022 novel by John Banville
The Singularities is a novel by the Irish author John Banville, published in 2022 by Alfred A. Knopf. It is based on characters and themes from the author's
The_Singularities
Use of grammar in a language to express number
more"). English and many other languages present number categories of singular or plural. Some languages also have a dual, trial and paucal number or
Grammatical_number
Hungarian and American mathematician and physicist (1903–1957)
ISBN 978-0-8176-4775-9. Lord, Steven; Sukochev, Fedor; Zanin, Dmitriy (2012). Singular Traces: Theory and Applications (1 ed.). De Gruyter. doi:10.1515/9783110262551
John_von_Neumann
Key results in general relativity on gravitational singularities
The Penrose–Hawking singularity theorems (after Roger Penrose and Stephen Hawking) are a set of results in general relativity that attempt to answer the
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Compact operator for which a finite trace can be defined
used to compute the trace. This trace of trace-class operators generalizes the trace of matrices studied in linear algebra. All trace-class operators are
Trace_class
Complex-valued function
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). The function
Fredholm_determinant
Natural number
Arabic numeral. Linguistically, in English, "one" is a determiner for singular nouns and a gender-neutral pronoun. In mathematics, 1 is the multiplicative
1
General relativity model near spacetime singularities
relativity has a page on the topic of: BKL singularity A Belinski–Khalatnikov–Lifshitz (BKL) singularity is a model of the dynamic evolution of the universe
BKL_singularity
Japanese kaiju television series
Godzilla Singular Point (Japanese: ゴジラ S.P ＜シンギュラポイント＞, Hepburn: Gojira Shingyura Pointo) is a Japanese anime television series directed by Atsushi Takahashi
Godzilla_Singular_Point
Function that measures dissimilarity between two probability distributions
chains with positive equilibrium P ∗ {\displaystyle P^{*}} and is of the trace-form ( H ( P ) = ∑ i f ( P i , P i ∗ ) {\displaystyle H(P)=\sum _{i}f(P_{i}
F-divergence
ISBN 978-3-11-019805-8 S. Lord, F. A. Sukochev. D. Zanin (2012). Singular traces: theory and applications. Berlin: De Gruyter. doi:10.1515/9783110262551
Commutator_subspace
West Germanic language
and singular, and are the only pronouns available for the plural. In the singular, the they/them series (sometimes with the addition of the singular-specific
English_language
the writing scripts of the six kingdoms has been abolished and only the singular script of the Qin Kingdom should be used. He mandates that all new writing
List of The Legend of Qin episodes
List_of_The_Legend_of_Qin_episodes
Field-equations in general relativity
}-{\frac {1}{2}}T\,g_{\mu \nu }\right).} Reversing the trace again would restore the original EFE. The trace-reversed form may be more convenient in some cases
Einstein_field_equations
Metric in quantum mechanics
especially quantum information and the study of open quantum systems, the trace distance is a metric on the space of density matrices and gives a measure
Trace_distance
Term in quantum mechanics
s_{j}(A)\geq 0} are the (always real and non-negative) singular values of A {\displaystyle A} , as in the singular value decomposition. The inequality is saturated
Fidelity_of_quantum_states
Trace fossil
Fodinichnia /ˌfɒdɪˈnɪkniə/ (singular fodinichnion) are trace fossils formed by deposit feeders as they excavate the sediment in search of food. They tend
Fodinichnia
Notion in statistics
be regular; otherwise, the statistical model is said to be singular. Examples of singular statistical models include the following: normal mixtures, binomial
Fisher_information
(2011) Albeverio, S.; Guido, D.; Ponosov, A.; Scarlatti, S. (1996). "Singular traces and compact operators". J. Funct. Anal. 137 (2): 281–302. doi:10.1006/jfan
Criticism of nonstandard analysis
Criticism_of_nonstandard_analysis
Citizens or residents of Mauritius
template Infobox ethnic group is being considered for merging. › Mauritians (singular Mauritian; French: Mauricien; Creole: Morisien) are nationals of the Republic
Mauritians
Polish–Lithuanian magnate family
Russian: Тышкевичи, singular: Тышкевич) was a wealthy and influential Polish-Lithuanian magnate family of Ruthenian origin, with roots traced to the times of
Tyszkiewicz_family
2026 American comedy horror television series
of Easttown meets Schitt's Creek, but with something else that makes it singular". Variety's Alison Herman wrote, "Widow's Bay may not make the best tourist
Widow's_Bay
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
Trace_inequality
contains exclusively Gaulish names, although it shows that Latinized genitive singular ending -i. Another inscription reading Frontu Tarbetis[o]nios contains
Dialects_of_Latin
American actress
shows, including Sex and the City, Strong Medicine, Rescue Me, Without a Trace, Crossing Jordan, CSI: Miami, Medium and Law & Order: Criminal Intent
Mireille_Enos
22-Apr-76 2048 Dust-up at the Royal Disco and Other Incredible Stories: The Singular Story of the Statue 23-Apr-76 2049 Rebecca's World: Part 1 - The Telescope
List_of_Jackanory_episodes
ISBN 978-0-8218-3581-4. S. Lord, F. A. Sukochev. D. Zanin (2012). Singular traces: theory and applications. Berlin: De Gruyter. ISBN 978-3-11-026255-1
Calkin_correspondence
Word that substitutes for a noun or noun phrase
cross-linguistically. An example of a pronoun is "you", which can be either singular or plural. Sub-types include personal and possessive pronouns, reflexive
Pronoun
Compact astronomical body
relativity also predicts that every black hole should have a central singularity, where the curvature of spacetime is infinite. Objects whose gravitational
Black_hole
Grammatical number
extremely complex grammatical number systems, with singular, dual, paucal, greater paucal, and plural. Traces of the dual and paucal can be found in some Slavic
Plural
Matrix with a multiplicative inverse
In linear algebra, an invertible matrix (non-singular, non-degenerate or regular) is a square matrix that has an inverse. In other words, if a matrix is
Invertible_matrix
Hunting and dietary habits of the golden eagle
killing a young female sika deer weighing 40 to 50 kg (88 to 110 lb), a singular event to capture on film since eagles hunts of even regular prey are difficult
Dietary biology of the golden eagle
Dietary_biology_of_the_golden_eagle
Most widely spoken of all Sámi languages
in the stem, where the strong grade appears in the nominative singular, illative singular and essive, while the weak grade appears in the remaining forms
Northern_Sámi
2021 book by Oliver Krüger
God, Evolution, and the Singularity in Post- and Transhumanism is a study by German religious scholar Oliver Krüger. Krüger traces the origins, context,
Virtual Immortality – God, Evolution, and the Singularity in Post- and Transhumanism
Virtual_Immortality_–_God,_Evolution,_and_the_Singularity_in_Post-_and_Transhumanism
Aspect of photography history
2002. ISSN 0032-4582 "Modern Tests: Yashica Samurai: Double Frame 35 is Singular Success," pp. 50–57. Modern Photography, Volume 53, Number 4; April 1989
History of the single-lens reflex camera
History_of_the_single-lens_reflex_camera
Epic cycle of the Scythian religion
Scythian genealogical myth have been retold by Greco-Roman authors, which all traced the origin of the Scythians to the god Targī̆tavah and to the Scythian Snake-Legged
Scythian_genealogical_myth
Language of the Basque people
persons, five singular and three plural, with the exception of nor-nori-nork in which the absolutive can be only third-person singular or plural. The
Basque_language
Generalized matrix decomposition for Lie groups and Lie algebras
It generalizes the polar decomposition or singular value decomposition of matrices. Its history can be traced to the 1880s work of Élie Cartan and Wilhelm
Cartan_decomposition
based on moral power, the Mandate of Heaven. In Zhou theology, Tian had no singular earthly progeny, but bestowed divine favour on virtuous rulers. Zhou kings
History_of_religion_in_China
2015 single by Chvrches
"Leave a Trace" is a song by Scottish synth-pop band Chvrches from their second studio album Every Open Eye. It was released as the band's first official
Leave_a_Trace
Language
fihu "cattle", follows the declension, and exists only in the singular. The only trace of a feminine u-declension is in the word hant "hand", declined
Old_High_German_declension
West Germanic language
example: Masculine singular: "des duivels" (lit: "of the devil") (common proverbial meaning: Seething with rage) Feminine singular: "het woordenboek der
Dutch_language
Classical Greek phrase meaning 'come and take [them]'
λαβέ, is the second person singular aorist imperative of λαμβάνω "take; grasp, seize". The entire phrase is thus in the singular, i.e. Leonidas is depicted
Molon_labe
Currency of India
and the erstwhile British Raj. The rupee is subdivided into 100 paise (singular: paisa). The issuance of the currency is controlled by the Reserve Bank
Indian_rupee
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
18 September 1908. Retrieved 30 October 2024 – via Wikisource. It is a singular thing that Selfridge designed the propeller of the Baldwin airship, which
List of unusual deaths in the 20th century
List_of_unusual_deaths_in_the_20th_century
Process in linear algebra
re-ordering. The Schmidt decomposition is essentially a restatement of the singular value decomposition in a different context. Fix orthonormal bases { e 1
Schmidt_decomposition
{\displaystyle {\mathcal {M}}} be a finite factor with the canonical normalized trace τ {\displaystyle \tau } and let X {\displaystyle X} be an invertible operator
Fuglede−Kadison_determinant
Tensor in differential geometry
converge. Formally, it is a symmetric rank-two tensor obtained by taking a trace of the Riemann curvature tensor of a Riemannian or pseudo-Riemannian metric
Ricci_curvature
End of the human species
possible ending of the human species, either by population decline due to singular natural events—for example, space irradiation, asteroid impact, or large-scale
Human_extinction
History of the commercial TV and radio network
the style of talking directly to the listener as an individual, with a singular "you" rather than phrases like "Now, folks..." or "Yes, friends...". His
History_of_CBS
Yudkowsky – American artificial intelligence researcher concerned with the singularity and an advocate of friendly artificial intelligence Hertha Marks Ayrton
List of Jewish atheists and agnostics
List_of_Jewish_atheists_and_agnostics
Mapping theorem in topology
the matrix traces of the linear maps induced by f {\displaystyle f} on H k ( X , Q ) {\displaystyle H_{k}(X,\mathbb {Q} )} , the singular homology groups
Lefschetz_fixed-point_theorem
Non-standard Latin spoken in ancient Rome
that it was easy to confuse the singular nominative with the plural oblique, and the plural nominative with the singular oblique, this case system ultimately
Vulgar_Latin
American singer and songwriter (born 1958)
Billboard Hot 100 and holds the record for the most chart-toppers on a singular Billboard chart. Her accolades include seven Grammy Awards, two Golden
Madonna
Computer-aided geometric design
fields. The study of the iterative method with geometric meaning can be traced back to the work of scholars such as Dongxu Qi and Carl de Boor in the 1970s
Progressive-iterative approximation method
Progressive-iterative_approximation_method
item. Usage notes: in legal terminology, almost always plural. In the singular, it refers to the sealing material itself, such as wax. placé sous scellé
Glossary of French criminal law
Glossary_of_French_criminal_law
He had been linked to the crime through photos, forensic testing, and a singular washcloth, which led to his conviction of two-consecutive, ten-to twenty
List of wrongful convictions in the United States
List_of_wrongful_convictions_in_the_United_States
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}}
Schatten_norm
Ancestor of the Indo-European languages
position often varied among different members of a paradigm (e.g. between singular and plural of a verbal paradigm). Stressed syllables received a higher
Proto-Indo-European_language
Faculty of mind to store and retrieve data
large number of studies that found that consolidation of memories is not a singular event but are put through the process again, known as reconsolidation.
Memory
pronouns) Hindi Irish Italian - there is a trace of the neuter in some nouns and personal pronouns. E.g.: singular l'uovo, il dito; plural le uova, le dita
List of languages by type of grammatical genders
List_of_languages_by_type_of_grammatical_genders
Commercial building in Manhattan, New York
Moin, David (August 14, 2012). "Bergdorf Goodman at 111: Celebrating a Singular Anniversary". WWD. Archived from the original on August 5, 2024. Retrieved
Bergdorf_Goodman_Building
American sex offender and cult leader (born 1955)
the community and her escape as well as her accounts in the Jeffs trial Singular, Stephen (July 7, 2009). When Men Become Gods: Mormon Polygamist Warren
Warren_Jeffs
Country in South Asia
achievements since independence in sustaining freedom and democracy have been singular among the world's new nations." Stein, Burton (2012). Arnold, David (ed
India
Iron Age culture in central Italy
used from the 7th-century BCE to around the 5th-century BCE consists of a singular dromos leading into a central area that splits off into separate rooms
Latial_culture
Theorem about zeros of holomorphic functions
travels along a closed curve C (not shown in the picture), f(z) and h(z) will trace out closed curves in the complex plane (shown in blue and red). So long
Rouché's_theorem
Dialect of Low German
and Ontario). Today, Plautdietsch is spoken in two major dialects that trace their division to what is now Ukraine. These two dialects are split between
Plautdietsch
Nonparametric spectral estimation method
In time series analysis, singular spectrum analysis (SSA) is a nonparametric spectral estimation method. It combines elements of classical time series
Singular_spectrum_analysis
Exploding Blood (爆血, Bakketsu), creating flames harmful to demons. Her most singular trait is her eventual immunity to sunlight, which makes her the primary
List of Demon Slayer: Kimetsu no Yaiba characters
List_of_Demon_Slayer:_Kimetsu_no_Yaiba_characters
and discovered a solution to the Einstein field equations containing singularities, which would later become known as the Schwarzschild solution. This
History_of_black_hole_physics
20th-century Italian saint, priest, stigmatist and mystic (1887–1968)
Palmarian pope Gregory XVII, the entirety of which is dedicated to this singular event. The town of San Giovanni Rotondo, where Padre Pio spent most of
Padre_Pio
Filling in missing entries of a matrix
least one observed entry per row and column of M {\displaystyle M} . The singular value decomposition of M {\displaystyle M} is given by U Σ V † {\displaystyle
Matrix_completion
Modern Hebrew, the singular word ba'alim ('owner') looks plural, but likewise takes a singular verb. A number of scholars have traced the etymology to the
Names_of_God_in_Judaism
2025 animated series
the works of Ray Harryhausen as well as Gillis' life in Florida. StuGo's singular season premiered on January 11, 2025, on Disney Channel, and concluded
StuGo
Language of ancient Sumer and Babylon
singular, seems to include the ventive prefix (Jagersma 2010: 390, 410). Only attested in late texts. For the dative and the directive, the singular form
Sumerian_language
Isomorphism between the tangent and cotangent bundles of a manifold
on Poisson manifolds, the relationship may fail to be an isomorphism at singular points, and so, for these cases, is technically only a homomorphism. In
Musical_isomorphism
Graphene-Based Brain Implant Can Peer Deep Into the Brain From Its Surface". Singularity Hub. 11 January 2024. Retrieved 15 January 2024. Ramezani, Mehrdad; Kim
2024_in_science
Celebration honouring mothers
International Association. She specifically noted that "Mother's" should "be a singular possessive, for each family to honor its own mother, not a plural possessive
Mother's_Day
Chemical element with atomic number 18 (Ar)
The name "argon" is derived from the Ancient Greek word ἀργόν, neuter singular form of ἀργός meaning 'lazy' or 'inactive', as a reference to the fact
Argon
Family of languages and dialects Indigenous to North Africa
Berber languages, with gender being feminine or masculine, number being singular or plural, and case being in the construct or free state. Some Arabic borrowings
Berber_languages
Election in the Spanish region of Andalusia
elecciones andaluzas para hacer un "plebiscito" sobre Sánchez y la financiación singular". El Mundo (in Spanish). Madrid. Retrieved 21 October 2025. Lamet, Juanma
2026 Andalusian regional election
2026_Andalusian_regional_election
Ethio-Semitic language
between singular (I) and plural (we), whereas for second and third persons, there is a distinction between singular and plural and within the singular a further
Amharic
Equation in Fourier analysis
which generates the unitary group. For the Laplacian, the "wave trace" has singular support contained in the set of lengths of periodic geodesics; this
Poisson_summation_formula
2025 studio album by Cardi B
with Cardi's public persona, which she describes as "never [having] been singular" and that "multiplicity is her identity, and [Am I the Drama?] reflects
Am_I_the_Drama?
Archaeology. 79 101704. 101704. doi:10.1016/j.jaa.2025.101704. Prat, S. (2025). "Singular or plural Oldowan tool-makers during the Lower Pleistocene in eastern Africa
2025_in_paleomammalogy
Peruvian Indigenous cleric and professor
constant opinion of all that Plato held the ideas to be really separate from singulars and exist by themselves. He added that: the thesis I am proposing, as
Juan_de_Espinosa_Medrano
that it could only be envisaged as a last extremity". France even showed singular audacity by opposing, at the UN Security Council, the US project of invasion
Foreign_relations_of_Iraq
Country in West Asia
communities (hamaynkner, singular hamaynk). Each community is self-governing and consists of one or more settlements (bnakavayrer, singular bnakavayr). Settlements
Armenia
American serial killer (born 1945)
Archived from the original on December 29, 2014. Retrieved January 21, 2015. Singular, Stephen (March 27, 2007). Unholy Messenger: The Life and Crimes of the
Dennis_Rader
Free online crowdsourced encyclopedia
Convertino, Gregorio; Chi, Ed H.; Pirolli, Peter (October 25, 2009). "The singularity is not near: slowing growth of Wikipedia". Proceedings of the 5th International
Wikipedia
SINGULAR TRACE
SINGULAR TRACE
Girl/Female
Muslim
Unique, Singular, Exclusive
Girl/Female
Indian
Unique, Singular, Exclusive
Girl/Female
Arabic, Gujarati, Indian, Kannada, Kashmiri, Muslim, Sindhi
Unique; Singular; Sole; Exclusive
Girl/Female
Arabic, Muslim
Singular; Unparalleled; Alone; Unique
Girl/Female
Muslim
Unique, Singular, Exclusive
Girl/Female
Arabic, Muslim
Unique; Singular; Single
Girl/Female
Arabic, Muslim
Unique; Singular
Girl/Female
Arabic, Muslim
Wish; Desire; Purpose; Use; Aim; Singular of Marib
Girl/Female
Muslim
Unique, Singular, Exclusive
Girl/Female
Arabic, Muslim
Present; Gift; Singular of Nihel
Girl/Female
Arabic, Muslim
Present; Gift; Singular of Nihel
Boy/Male
Afghan, Arabic, Danish, French, Kashmiri, Muslim, Pashtun, Sindhi
Singular; Unique; Alone; Exclusively; Unequalled; Exceptional; Peerless
Surname or Lastname
English
English : from Middle English sengler, syngler ‘singular’ (Old French se(i)ngler), perhaps a nickname for a solitary person.German : topographic name for a valley dweller, from a diminutive of Middle High German senke ‘valley’ + the suffix -er, denoting an inhabitant.German : habitational name for someone from Singeln near Waldshut.German : variant of Sing 1.
Biblical
lot, singular of Purim (lots, as in Cleromancy [casting of lots])
Girl/Female
Indian
Unique, Singular, Exclusive
Girl/Female
Indian
Unique, Singular, Exclusive
Girl/Female
Celtic
Mythical daughter of Lyr.
Girl/Female
Muslim
Unique, Singular
Boy/Male
Muslim/Islamic
Singular exclusive, unequalled
Girl/Female
Indian
Unique, Singular
SINGULAR TRACE
SINGULAR TRACE
Boy/Male
Tamil
Charuchandra | சாரà¯à®šà®‚தà¯à®°
Beautiful Moon
Biblical
a bending of sin
Male
English
Middle English form of French Yvain, YWAIN means "well born." In Arthurian legend, this is the name of a Knight of the Round Table, a son of King Urien. He is said by some to be the son of Morgan le Fay, making him Arthur's nephew. He has a half-brother named after him, and a twin sister named Morvydd. In Welsh legend, his name was Owain, which has a different meaning.Â
Boy/Male
Shakespearean American English German
King Henry V' Soldier in the King's army.
Girl/Female
Indian
One of great courage, Boldness
Female
French
Feminine form of French Valère, VALÉRIE means "to be healthy, to be strong."Â
Girl/Female
Indian
Golden doll
Boy/Male
Tamil
To enter
Female
English
Variant spelling of English Ailsa, AILSE means "elf victory."
Female
English
Modern elaborated form of English Gina, LAGINA means "earth-worker, farmer."Â
SINGULAR TRACE
SINGULAR TRACE
SINGULAR TRACE
SINGULAR TRACE
SINGULAR TRACE
n.
Singular; wonderful; extraordinary.
n.
See Kickshaws, the correct singular.
adv.
In a singular manner; in a manner, or to a degree, not common to others; extraordinarily; as, to be singularly exact in one's statements; singularly considerate of others.
a.
Being alone; belonging to, or being, that of which there is but one; unique.
n.
The singular number, or the number denoting one person or thing; a word in the singular number.
a.
Each; individual; as, to convey several parcels of land, all and singular.
a.
Measured by an angle; as, angular distance.
n.
Any one of numerous species of brachiopod shells belonging to the genus Lingula, and related genera. See Brachiopoda, and Illustration in Appendix.
n.
An individual instance; a particular.
a.
Fig.: Lean; lank; raw-boned; ungraceful; sharp and stiff in character; as, remarkably angular in his habits and appearance; an angular female.
adv.
So as to express one, or the singular number.
a.
Rather queer; somewhat singular.
n.
Anything singular, rare, or curious.
a.
Denoting one person or thing; as, the singular number; -- opposed to dual and plural.
a.
Relating to an angle or to angles; having an angle or angles; forming an angle or corner; sharp-cornered; pointed; as, an angular figure.
a.
Of or pertaining to an island; of the nature, or possessing the characteristics, of an island; as, an insular climate, fauna, etc.
a.
Of or pertaining to the people of an island; narrow; circumscribed; illiberal; contracted; as, insular habits, opinions, or prejudices.
a.
Standing by itself; out of the ordinary course; unusual; uncommon; strange; as, a singular phenomenon.
a.
Distinguished as existing in a very high degree; rarely equaled; eminent; extraordinary; exceptional; as, a man of singular gravity or attainments.
adv.
Strangely; oddly; as, to behave singularly.