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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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
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
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
(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
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
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
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
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
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
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
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
{\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
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
contains exclusively Gaulish names, although it shows that Latinized genitive singular ending -i. Another inscription reading Frontu Tarbetis[o]nios contains
Dialects_of_Latin
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Collection of character sketches
appearance, he is like a cross between Charles Fox and Benjamin Franklin, "a singular mixture of boyish simplicity and the venerableness of age." He has no taste
The_Spirit_of_the_Age
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
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
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
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
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
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
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
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
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
alongside in many dialects. Polish generalized the genitive singular ending -a; the only trace of *-e of *-n, *-nt stems is the softening of the final stem
History of the Polish language
History_of_the_Polish_language
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
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
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
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
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
Abbreviation of "greatest of all time"
greatest athlete or inclusion in cross-sports commentary as an all-time singular greatest athlete has been discussed. Players themselves have also commented
GOAT_(sports_culture)
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
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?
primarily located in the insular and frontal opercular regions. Gyri (singular gyrus) The raised ridges or folds of the cerebral cortex. They increase
Glossary_of_neuroscience
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
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
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
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
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
Hypothetical astronomical object
repulsive "force" is strong enough to stop the star's collapse well before a singularity is formed and, indeed, well before the Planck scale for distance: for
Planck_star
DLC for the video game Destiny 2 released from 2017 to 2026
30th Anniversary Pack. Battlegrounds and strikes were merged into one singular playlist called the Vanguard Operations. Astral Alignment from Season of
Destiny 2 post-release content
Destiny_2_post-release_content
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
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
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
Indo-European language of the Italic branch
singular. If it ends in -ius (such as fīlius), the ending is just -ī (filī), as distinct from the nominative plural (filiī) in the vocative singular:
Latin
South Korean boy band
Middle Eastern flavours, traces of indie pop, tropical house, synthwave, and trap-infused slow jams they have created a strong singular identity without sacrificing
Ateez
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
Trace radiation from the early universe
contaminated multipoles are [the quadrupole and octupole], which most closely trace the galactic plane morphology." O'Dwyer, I.; Eriksen, H. K.; Wandelt, B
Cosmic_microwave_background
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
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)
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
Hypothetical object of spacetime
general relativity, a white hole is a hypothetical region of spacetime and singularity that cannot be entered from the outside, although energy, matter, light
White_hole
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
Partial differential equation
Simon Brendle and Richard Schoen. Following the possibility that the singularities of solutions of the Ricci flow could identify the topological data predicted
Ricci_flow
Closed lexical category of the English language
archaic forms can be traced back to Middle English pronouns via Early Modern English. An archaic set of second-person singular pronouns are thou, thee
Personal_pronouns_in_English
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
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. The
Musical_isomorphism
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
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
// 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
SINGULAR TRACE
SINGULAR TRACE
Girl/Female
Arabic, Muslim
Present; Gift; Singular of Nihel
Girl/Female
Muslim
Unique, Singular, Exclusive
Girl/Female
Indian
Unique, Singular
Girl/Female
Arabic, Muslim
Present; Gift; Singular of Nihel
Girl/Female
Arabic, Muslim
Unique; Singular; Single
Girl/Female
Muslim
Unique, Singular, Exclusive
Girl/Female
Indian
Unique, Singular, Exclusive
Girl/Female
Celtic
Mythical daughter of Lyr.
Girl/Female
Arabic, Gujarati, Indian, Kannada, Kashmiri, Muslim, Sindhi
Unique; Singular; Sole; Exclusive
Boy/Male
Muslim/Islamic
Singular exclusive, unequalled
Girl/Female
Indian
Unique, Singular, Exclusive
Girl/Female
Muslim
Unique, Singular
Biblical
lot, singular of Purim (lots, as in Cleromancy [casting of lots])
Girl/Female
Arabic, Muslim
Singular; Unparalleled; Alone; Unique
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.
Girl/Female
Muslim
Unique, Singular, Exclusive
Girl/Female
Arabic, Muslim
Unique; Singular
Girl/Female
Arabic, Muslim
Wish; Desire; Purpose; Use; Aim; Singular of Marib
Girl/Female
Indian
Unique, Singular, Exclusive
Boy/Male
Afghan, Arabic, Danish, French, Kashmiri, Muslim, Pashtun, Sindhi
Singular; Unique; Alone; Exclusively; Unequalled; Exceptional; Peerless
SINGULAR TRACE
SINGULAR TRACE
Boy/Male
Muslim
Boy/Male
Hindu, Indian, Marathi
A Voice of King
Boy/Male
Sikh
Praise of the glorious protector, Lord Krishna
Boy/Male
Hindu, Indian
King
Boy/Male
Tamil
A strom God
Boy/Male
Arabic, Muslim, Pashtun
Lion Heart
Boy/Male
Indian, Punjabi, Sikh
The Youth
Girl/Female
Tamil
The mirror
Girl/Female
Arabic
Star
Boy/Male
Tamil
Most Love
SINGULAR TRACE
SINGULAR TRACE
SINGULAR TRACE
SINGULAR TRACE
SINGULAR TRACE
n.
The singular number, or the number denoting one person or thing; a word in the singular number.
n.
Singular; wonderful; extraordinary.
a.
Being alone; belonging to, or being, that of which there is but one; unique.
n.
Anything singular, rare, or curious.
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.
Fig.: Lean; lank; raw-boned; ungraceful; sharp and stiff in character; as, remarkably angular in his habits and appearance; an angular female.
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.
adv.
So as to express one, or the singular number.
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.
Rather queer; somewhat singular.
a.
Denoting one person or thing; as, the singular number; -- opposed to dual and plural.
a.
Each; individual; as, to convey several parcels of land, all and singular.
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.
Standing by itself; out of the ordinary course; unusual; uncommon; strange; as, a singular phenomenon.
a.
Of or pertaining to the people of an island; narrow; circumscribed; illiberal; contracted; as, insular habits, opinions, or prejudices.
a.
Measured by an angle; as, angular distance.
a.
Of or pertaining to an island; of the nature, or possessing the characteristics, of an island; as, an insular climate, fauna, etc.