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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
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
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)
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
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
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
Hypothetical event
The technological singularity, often simply called the singularity, is a hypothetical event in which technological growth accelerates beyond human control
Technological_singularity
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
contains exclusively Gaulish names, although it shows that Latinized genitive singular ending -i. Another inscription reading Frontu Tarbetis[o]nios contains
Dialects_of_Latin
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
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
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
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
(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
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
Nobel Prize nominees for Literature
idealism and humanity, its stimulating satire often being infused with a singular poetic beauty" This nomination was retrieved for having arrived too late
List of nominees for the Nobel Prize in Literature
List_of_nominees_for_the_Nobel_Prize_in_Literature
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
Traditional Sufi chant
invocation of the Divine name Allah and Hū, the Qur'anic third-person singular pronoun referring to Allah and widely employed in Sufi devotional practice
Allah_Hoo
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
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
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
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
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
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
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
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
Country in Central Europe
the Czech Republic has been divided into thirteen regions (Czech: kraje, singular kraj) and the capital city of Prague. Every region has its own elected
Czech_Republic
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
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
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
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
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
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
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
{\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
History of the city of Ningbo, China
could scarcely have believed the Chinese capable of perpetrating. The singular feature of it is, that it should have been directed in such a marked way
History_of_Ningbo
Early Chinese religious history
refer to any spirit. While agreeing with Eno against the existence of a singular god, John C. Didier opposes Eno's position that the Shang conceived of
Religion_of_the_Shang_dynasty
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
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
Portuguese-based creole of Cape Verde
standardized.[citation needed] The history of Cape Verdean Creole is hard to trace due to a lack of written documentation and to ostracism during the Portuguese
Cape_Verdean_Creole
German chapbook
15). In another variant from Mallorca, Sa Cadeneta (Das Kettchen), is singular in that the peasant brother uses the fruits (pears and figs) before the
Fortunatus_(book)
Linguistic system of noun classification
the singular, however, the issue frequently arises when a person of unspecified or unknown gender is being referred to. In this case it the Singular they
Grammatical_gender
Void between celestial bodies
about airspace violations. It has been argued for setting no specified singular altitude in international law, instead applying different limits depending
Outer_space
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
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
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
Process of word formation, by alteration to express grammatical categories
will lead', includes the suffix -am, expressing person (first), number (singular), and tense-mood (future indicative or present subjunctive). The use of
Inflection
Biographies of famous Greeks and Romans by Plutarch
and Cicero. There are also four singular Lives, recounting the stories of Artaxerxes, Aratus, Galba, and Otho. Traces of other biographies point to an
Parallel_Lives
Gallo-Romance dialect continuum
singular form (nominative and oblique) ending in -e. They can be further subdivided into two subclasses, based on the masculine nominative singular form
Old_French
Square root of the determinant of a skew-symmetric square matrix
The following formula applies even if the matrix A {\displaystyle A} is singular for some values of the variable x {\displaystyle x} : ∂ ∂ x k pf ( A
Pfaffian
2018 novel by Greer Hendricks and Sarah Pekkanen
over before the first reveal, but it’s worth the wait, if only for its singularity. Then the twists come fast and furious." In 2017 the film rights for
The_Wife_Between_Us
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
1990s art movement in Brooklyn, New York City
shifting urban environment. Immersionism, in other words, was not just a singular event bounded by space and time. Nor was Immersionist culture an idealization
Brooklyn_Immersionists
Group of languages
from the above allophonic fricatives. Replacement of the second-person singular preterite ending -t with -ī (indicative and subjunctive mood). For more
West_Germanic_languages
Type of continuous linear operator
with singular values s n = 1 / n {\displaystyle s_{n}=1/n} is compact and Hilbert–Schmidt but not trace class, while an operator with singular values
Compact_operator
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
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
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?
Phonetic phenomenon in Uralic languages
difference between giella and giela ('language', nominative and genitive singular respectively) is the grade; the final consonant that originally closed
Consonant_gradation
// Пушкин и его окружение. — 1989 (текст)". "Letter From Baltimore. - Singular Coincidence". The Evening Telegraph (Philadelphia, Pa.). 22 January 1866
List of serial killers before 1900
List_of_serial_killers_before_1900
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
notes that "In none of the cases of 'idiot savant' have I been able to trace any history of a like faculty in the parents or in the brothers and sisters
History_of_autism
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
Extinct Italic language of central Italy
accusative singular and plural: the neuter nominative and accusative singular are identical with each other and the masculine accusative singular, while the
Umbrian_language
American automobile racing company
Canada, Mexico, Brazil, and Europe. NASCAR, and stock car racing as a whole, traces its roots back to moonshine runners during Prohibition, who grew to compete
NASCAR
Arabic greeting
appropriate enclitic pronoun to address a person in the masculine and feminine singular form, the dual form, or the feminine plural form. The conjugations are
As-salamu_alaykum
East Asian ethnic group
primary formative influence in Chinese culture and history. The Han Chinese trace their ancestry and culture to the Huaxia people, a confederation of agricultural
Han_Chinese
Ethnic group in West Africa
Ghana. Oral traditions and archaeological evidence indicate that the Akan trace their origins to the forest and forest–savanna transition zone, with early
Akan_people
department store chain in New Zealand following the closure of DFS (a singular David Jones store remains in operation at Westfield Newmarket). It was
Department_stores_by_country
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
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
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
Citizens or residents of Mauritius
Mauritians (singular Mauritian; French: Mauricien; Creole: Morisien) are nationals of the Republic of Mauritius and their descendants. Given its geographic
Mauritians
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
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
Renaissance art in Florence
Rosselli, was an ingenious and imaginative artist, capable of creating singular and bizarre works. His work explores religious painting, portraits and
Florentine_Renaissance_art
Northwest Semitic supreme deity
'powers'. In the Hebrew texts this word is interpreted as being semantically singular for "god" by biblical commentators. The documentary hypothesis theorizes
El_(deity)
Castillo Oreja, Miguel Ángel (2000). La Iglesia del Buen Suceso: Un edificio singular en la Historia de la Puerta del Sol de Madrid. Madrid: Artes Gráf. Municipales
History_of_the_Puerta_del_Sol
West Germanic language
in western New York (Bergholz, New York), a community of Lutherans who trace their immigration from Pomerania in the 1840s, hold quarterly "Plattdeutsch
Low_German
Political phrase related to the Palestine region
under an Israeli siege. All of them suffer from a range of policies in a singular system of discrimination and apartheid—a system that can only be challenged
From_the_river_to_the_sea
SINGULAR TRACE
SINGULAR TRACE
Girl/Female
Arabic, Muslim
Present; Gift; Singular of Nihel
Biblical
lot, singular of Purim (lots, as in Cleromancy [casting of lots])
Girl/Female
Arabic, Muslim
Unique; Singular; Single
Girl/Female
Arabic, Muslim
Present; Gift; Singular of Nihel
Girl/Female
Muslim
Unique, Singular, Exclusive
Girl/Female
Muslim
Unique, Singular, Exclusive
Girl/Female
Arabic, Muslim
Wish; Desire; Purpose; Use; Aim; Singular of Marib
Girl/Female
Indian
Unique, Singular, Exclusive
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.
Boy/Male
Muslim/Islamic
Singular exclusive, unequalled
Girl/Female
Muslim
Unique, Singular, Exclusive
Girl/Female
Arabic, Muslim
Unique; Singular
Boy/Male
Afghan, Arabic, Danish, French, Kashmiri, Muslim, Pashtun, Sindhi
Singular; Unique; Alone; Exclusively; Unequalled; Exceptional; Peerless
Girl/Female
Arabic, Gujarati, Indian, Kannada, Kashmiri, Muslim, Sindhi
Unique; Singular; Sole; Exclusive
Girl/Female
Indian
Unique, Singular, Exclusive
Girl/Female
Muslim
Unique, Singular
Girl/Female
Celtic
Mythical daughter of Lyr.
Girl/Female
Indian
Unique, Singular, Exclusive
Girl/Female
Indian
Unique, Singular
Girl/Female
Arabic, Muslim
Singular; Unparalleled; Alone; Unique
SINGULAR TRACE
SINGULAR TRACE
Boy/Male
Tamil
Hemchander | ஹேமசஂதர
Golden Moon
Boy/Male
Indian
The son of Ali (The son of Ali)
Boy/Male
Indian
Collator
Boy/Male
Native American
clay.
Girl/Female
Indian
Pretty; Holy Message of Saint; Cleaver
Girl/Female
Indian
Night.
Boy/Male
Hindu, Indian
Conqueror of Madhu
Girl/Female
Hindu
Boy/Male
German
Wolf Ruler
Girl/Female
Indian
Good wish, Spring season (Vasanth Ritu)
SINGULAR TRACE
SINGULAR TRACE
SINGULAR TRACE
SINGULAR TRACE
SINGULAR TRACE
a.
Being alone; belonging to, or being, that of which there is but one; unique.
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 the people of an island; narrow; circumscribed; illiberal; contracted; as, insular habits, opinions, or prejudices.
a.
Of or pertaining to an island; of the nature, or possessing the characteristics, of an island; as, an insular climate, fauna, etc.
n.
Any one of numerous species of brachiopod shells belonging to the genus Lingula, and related genera. See Brachiopoda, and Illustration in Appendix.
a.
Standing by itself; out of the ordinary course; unusual; uncommon; strange; as, a singular phenomenon.
a.
Each; individual; as, to convey several parcels of land, all and singular.
n.
See Kickshaws, the correct singular.
n.
Anything singular, rare, or curious.
n.
An individual instance; a particular.
n.
Singular; wonderful; extraordinary.
a.
Measured by an angle; as, angular distance.
a.
Rather queer; somewhat 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.
Distinguished as existing in a very high degree; rarely equaled; eminent; extraordinary; exceptional; as, a man of singular gravity or attainments.
n.
The singular number, or the number denoting one person or thing; a word in the singular number.
adv.
So as to express one, or the singular number.
a.
Fig.: Lean; lank; raw-boned; ungraceful; sharp and stiff in character; as, remarkably angular in his habits and appearance; an angular female.
adv.
Strangely; oddly; as, to behave singularly.
a.
Denoting one person or thing; as, the singular number; -- opposed to dual and plural.