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Lambda

From Wikipedia, the free encyclopedia

Eleventh letter in the Greek alphabet

This article is about the Greek letter. For other uses, seeLambda (disambiguation).

"Λ" redirects here; not to be confused withTurned v,ʎ,入, orЛ.

Αα	Alpha	Νν	Nu
Ββ	Beta	Ξξ	Xi
Γγ	Gamma	Οο	Omicron
Δδ	Delta	Ππ	Pi
Εε	Epsilon	Ρρ	Rho
Ζζ	Zeta	Σσς	Sigma
Ηη	Eta	Ττ	Tau
Θθ	Theta	Υυ	Upsilon
Ιι	Iota	Φφ	Phi
Κκ	Kappa	Χχ	Chi
Λλ	Lambda	Ψψ	Psi
Μμ	Mu	Ωω	Omega

Archaic local variants

Ϝϝ	Digamma	Ͱͱ	Heta
Ϻϻ	San	Ϙϙ	Koppa
Ͷͷ	Tsan Digamma	Ͳͳ	Sampi
Ϸϸ	Sho

Diacritics and other symbols

Numerals (Attic)

Related topics

Category

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Lambda(/ˈlæmdə/ ^ⓘ;^[1] uppercaseΛ, lowercaseλ;Greek:λάμ(β)δα,lám(b)da;Ancient Greek:λά(μ)βδα,lá(m)bda), sometimes renderedlamda,^[2]labda^[2] orlamma,^[2] is the eleventh letter of theGreek alphabet, representing thevoiced alveolar lateral approximantIPA:[l]; it derives from thePhoenician letterLamed, and gave rise toLatin L andCyrillic El (Л). In the system ofGreek numerals, lambda has a value of 30. The ancientgrammarians typically called itλάβδα (lắbdă,[lábda]) inClassical Greek times,^[3] whereas inModern Greek it isλάμδα (lámda,[ˈlamða]), while the spellingλάμβδα (lámbda) was used (to varying degrees) throughout the lengthy transition between the two.

Inearly Greek alphabets, the shape and orientation of lambda varied.^[4] Most variants consisted of two straight strokes, one longer than the other, connected at their ends. The angle might be in the upper-left, lower-left ("Western" alphabets) or top ("Eastern" alphabets). Other variants had a vertical line with a horizontal or sloped stroke running to the right. With the general adoption of theIonic alphabet, Greek settled on an angle at the top; the Romans put the angle at the lower-left.

The Greek alphabet on ablack figure vessel, with a Phoenician-lamed-shaped lambda. The gamma has the shape of modern lambda.

Symbol

Upper-case letter Λ

Examples of the symbolic use of uppercase lambda include:

Thelambda particle is a type ofsubatomic particle insubatomic particle physics.
Lambda is the set of logical axioms in theaxiomatic method of logical deduction infirst-order logic.
Uppercase Lambda is often used as a stylized form of uppercaseA, especially in science fiction.
There is a poetical allusion to the use of Lambda as ashield blazon by theSpartans.^{[citation needed]}^[5]
Lambda is thevon Mangoldt function in mathematicalnumber theory.^[6]
Lambda denotes thede Bruijn–Newman constant which is closely connected withRiemann's hypothesis.^[7]
Instatistics, lambda is used for thelikelihood ratio.
In statistics,Wilks's lambda is used in multivariate analysis of variance (MANOVA analysis) to compare group means on a combination of dependent variables.^[8]
In thespectral decomposition of matrices, lambda indicates thediagonal matrix of theeigenvalues of thematrix.
Incomputer science, lambda is the time window over which a process is observed for determining the working memory set for adigital computer'svirtual memory management.
Inastrophysics, lambda represents the likelihood that a small body will encounter aplanet or adwarf planet leading to a deflection of a significant magnitude. An object with a large value of lambda is expected to havecleared its neighbourhood, satisfying the currentdefinition of a planet.^[9]
Incrystal optics, lambda is used to represent a lattice period.
Inelectrochemistry, lambda denotes the "equivalentconductance" of anelectrolyte solution.^[10]
Incosmology, lambda is the symbol for thecosmological constant, a term added to some dynamical equations to account for theaccelerating expansion of the universe.^[11]
In optics, lambda denotes the grating pitch of aBragg reflector.^[12]
Inpolitics, the lambda is the symbol ofIdentitarianism, awhite nationalist movement that originated inFrance before spreading out to the rest ofEurope and later on toNorth America,Australia andNew Zealand. The Identitarian lambda represents theBattle of Thermopylae.

Lower-case letter λ

Lower-case lambda

Examples of the symbolic use of lowercase lambda include:

λ indicates thewavelength of anywave, especially inphysics,electrical engineering, andmathematics.^[13]
Inevolutionary algorithms, λ indicates the number of offspring that would be generated from μ current population in each generation. The terms μ and λ are originated fromevolution strategy notation.^[14]
λ indicates theradioactivity decay constant innuclear physics andradioactivity. This constant is very simply related (by a multiplicative constant) to thehalf-life of any radioactive material.
Inprobability theory, λ represents the density of occurrences within a time interval, as modelled by thePoisson distribution.^[15]
Inmathematical logic andcomputer science, λ is used to introduceanonymous functions expressed with the concepts oflambda calculus.
λ indicates aneigenvalue in the mathematics oflinear algebra.
In the physics of particles, lambda indicates thethermal de Broglie wavelength^[16]
In the physics ofelectric fields, lambda sometimes indicates the linearcharge density of a uniform line ofelectric charge (measured incoulombs per meter).
Lambda denotes aLagrange multiplier inmulti-dimensional calculus.^[17]
Insolid-state electronics, lambda indicates thechannel length modulation parameter of aMOSFET.^[18]
Inecology, lambda denotes the long-term intrinsic growth rate of a population.^[19] This value is often calculated as the dominant eigenvalue of the age/size classmatrix.
Informal language theory and in computer science, lambda denotes theempty string.^[20]
Lambda is a nonstandard symbol in theInternational Phonetic Alphabet for thevoiced alveolar lateral affricate[dɮ].^[21]
Lambda denotes theLebesgue measure inmathematical set theory.^[22]
TheGoodman and Kruskal's lambda instatistics indicates theproportional reduction in error when one variable's values are used to predict the values of another variable.^[23]
Lambda denotes theoxygen sensor in a vehicle that measures theair-to-fuel ratio in the exhaustgases of aninternal-combustion engine.^[24]
ALambda 4S solid-fuel rocket was used to launchJapan's first orbital satellite in 1970.^[25]
Lambda denotes thefailure rate of devices and systems inreliability theory, and it is measured in failure events per hour. Numerically, this lambda is also the reciprocal of themean time between failures.^[26]
In criminology, lambda denotes an individual's frequency ofoffences.^[27]
Inelectrochemistry, lambda also denotes theionic conductance of a given ion (the composition of the ion is generally shown as a subscript to the lambda character).
Inneurobiology, lambda denotes thelength constant (or exponential rate of decay) of theelectric potential across thecell membrane along a length of a nerve cell'saxon.
In the science and technology ofheat transfer, lambda denotes theheat of vaporization permole of material (a.k.a. its "latent heat").^[28]
In the technology and science ofcelestial navigation, lambda denotes thelongitude as opposed to the Roman letter "L", which denotes thelatitude.
A block style lambda is used as a recurring symbol in theValve computer game seriesHalf-Life,^[29] referring to the Lambda Complex of the fictionalBlack Mesa Research Facility, as well as making appearances in the sequelHalf-Life 2, and its subsequent prequelHalf-Life: Alyx as an in-universesymbol of resistance.^[30]
In 1970, a lowercase lambda was chosen byTom Doerr as the symbol of the New York chapter of theGay Activists Alliance.^[31]^[32] The lambda symbol became associated withgay liberation^[33]^[34] and recognized as anLGBTQ symbol for some time afterwards, being used as such by the International Gay Rights Congress in Edinburgh.^[35]
Golomb–Dickman constant^[36]
In continuum mechanics, lambda represents one of theLamé parameters, which is a material property that arises in stress-strain relationships.

Litra symbol

TheRomanlibra andByzantinelítra (λίτρα), which served as both the pound mass unit and liter volume unit, were abbreviated in Greek using lambda with modified forms of theiota subscript ⟨λͅ⟩. These are variously encoded in Unicode. TheAncient Greek Numbers Unicode block includes 10183GREEK LITRA SIGN (𐆃) as well as 𐅢, which is described as 10162GREEK ACROPHONIC HERMIONIAN TEN^[37] but was much more common as a form of the litra sign. A variant of the sign can be formed from 0338COMBINING LONG SOLIDUS OVERLAY and either 039BGREEK CAPITAL LETTER LAMDA (Λ̸) or 03BBGREEK SMALL LETTER LAMDA (λ̸).^[38]

Unicode

Unicode uses the (Modern Greek-based) spelling "lamda" in character names, instead of "lambda", due to "the pre-existing names in ISO 8859-7, as well as preferences expressed by the Greek National Body".^[39] Latin versions of lambda were added to Unicode in 2024 for theSalishan andWakashan languages inCanada.^[40]

U+039B ΛGREEK CAPITAL LETTER LAMDA (Λ)^[41]
U+03BB λGREEK SMALL LETTER LAMDA (λ)
U+1D27 ᴧGREEK LETTER SMALL CAPITAL LAMDA
U+2C96 ⲖCOPTIC CAPITAL LETTER LAULA
U+2C97 ⲗCOPTIC SMALL LETTER LAULA
U+A7DA ꟚLATIN CAPITAL LETTER LAMBDA
U+A7DB ꟛLATIN SMALL LETTER LAMBDA
U+1038D 𐎍UGARITIC LETTER LAMDA
U+1D6B2 𝚲MATHEMATICAL BOLD CAPITAL LAMDA^[a]
U+1D6CC 𝛌MATHEMATICAL BOLD SMALL LAMDA
U+1D6EC 𝛬MATHEMATICAL ITALIC CAPITAL LAMDA
U+1D706 𝜆MATHEMATICAL ITALIC SMALL LAMDA
U+1D726 𝜦MATHEMATICAL BOLD ITALIC CAPITAL LAMDA
U+1D740 𝝀MATHEMATICAL BOLD ITALIC SMALL LAMDA
U+1D760 𝝠MATHEMATICAL SANS-SERIF BOLD CAPITAL LAMDA
U+1D77A 𝝺MATHEMATICAL SANS-SERIF BOLD SMALL LAMDA
U+1D79A 𝞚MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL LAMDA
U+1D7B4 𝞴MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL LAMDA

^TheMATHEMATICAL characters should only be used in math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

See also

Look upΛ,λ,Ꟛ, orꟛ in Wiktionary, the free dictionary.

Barred lambda - ƛ
El (Cyrillic) – Л, л
Fraser alphabet#Consonants
Greek letters used in mathematics, science, and engineering
Half-Life (series)
Samsung, an electronics company that uses the glyph "Λ" in its logo as a styled "A".

References

^"lambda".Pronunciation.Oxford English Dictionary (Online ed.).Oxford University Press.doi:10.1093/OED/7055602338. (Subscription orparticipating institution membership required.)
^^a ^b ^c"lambda".Forms.Oxford English Dictionary (Online ed.).Oxford University Press.doi:10.1093/OED/1663278936. (Subscription orparticipating institution membership required.)
^Herbert Weir Smyth.A Greek Grammar for Colleges.I.1.c
^"Epigraphic Sources for Early Greek Writing".Poinikastas.CSAD.ox.ac.uk. Retrieved2011-10-03.
^Philodemus (2003).On Poems. Oxford University Press. p. 212.ISBN 9780199262854.
^Deza, Elena (2023).Perfect and amicable numbers. Selected chapters of number theory : special numbers. New Jersey: World Scientific. p. 79.ISBN 978-981-12-5962-3.Thevon Mangold function Λ(n) is defined as…
^Broughan, Kevin A. (2024).Equivalents of the Riemann hypothesis. Volume 3: Further steps towards resolving the Riemann hypothesis / Kevin Broughan (University of Waikato, New Zealand). Encyclopedia of mathematics and its applications. Cambridge, UK; New York; Port Melbourne, Victoria; New Delhi; Singapore: Cambridge University Press. p. 63.ISBN 978-1-009-38480-3.Now we can give the definition of the de Bruijn–Newman constant Λ.
^Everitt, Brian (2011).An introduction to applied multivariate analysis with R. Use R! Ser. Torsten Hothorn. New York: Springer New York.ISBN 978-1-4419-9649-7.In the current case of one-way MANOVA, it can be shown that the LR test statistic is a monotone function of what is called Wilks' lambda (Λ, capital Greek letter lambda):
^Wilkinson, John (2016).The Solar System in Close-Up. Astronomers' Universe Ser. Cham: Springer International Publishing AG. p. 7.ISBN 978-3-319-27627-4.American planetary scientists Alan Stern and Harold Levison introduced a parameter Λ (lambda) to express the likelihood of a body "clearing the neighborhood around its orbit".
^Kuhn, Reinhard; Hoffstetter-Kuhn, Sabrina (1993).Capillary electrophoresis: principles and practice. Springer Laboratory. Berlin Heidelberg: Springer. p. 12.ISBN 978-0-387-56434-0.According to the first Kohlrausch law, anions and cations contribute independently to the conductance, which means that the equivalent conductance Λ is the sum of the…
^Liddle, Andrew R. (2015).An introduction to modern cosmology (Third ed.). Chichester, West Sussex: John Wiley and Sons, Inc. p. 55.ISBN 978-1-118-50214-3.The cosmological constant Λ appears in the Friedman equation as an extra term,
^Pal, Bishnu, ed. (2010).Frontiers in Guided Wave Optics and Optoelectronics. Erscheinungsort nicht ermittelbar: IntechOpen. p. 352.ISBN 978-953-7619-82-4.The circular Bragg grating on the bottom DBR gives high reflection for Bragg wavelength which is decided, for first order grating in slab hollow waveguide [25], by the following equation… where Λ is grating pitch.
^Nelkon, Michael (1977).Fundamentals of Physics. St. Albans, Hertfordshire: Hart-Davis Educational. p. 329.
^Baragona, Roberto (2011).Evolutionary statistical procedures: an evolutionary computation approach to statistical procedures designs and applications. Statistics and computing. Francesco Battaglia, Irene Poli. Berlin: Springer. p. 16.ISBN 978-3-642-16217-6.…, and λ is the number of offsprings at each generation:
^Panik, Michael J. (2005).Advanced statistics from an elementary point of view. Boston: Elsevier/Academic Press. p. 260.ISBN 978-0-12-088494-0.Since λ is the mean number of occurrences per unit time of the Poisson process,
^Tabatabaian, Mehrzad; Rajput, R. K. (2018).Advanced thermodynamics: fundamentals, mathematics, applications. Dulles, Virginia Boston, Massachusetts New Delhi: Mercury Learning and Information. p. 434.ISBN 978-1-936420-27-8.A gas of atoms reaches quantum degeneracy when the matter waves of neighbouring atoms overlap – i.e. when the thermal de Broglie wavelength, λ, which means as the temperature falls,…
^Ito, Kazufumi (2008).Lagrange multiplier approach to variational problems and applications. Advances in Design and Control. K. Kunisch, Society for Industrial and Applied Mathematics. Philadelphia, Pa: Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, Pennsylvania 19104). pp. xii.ISBN 978-0-89871-649-8.Here the Lagrange multiplier λ is treated like an independent variable just likey andu.
^Wiegerink, Remco J. (1993).Analysis and synthesis of MOS translinear circuits. The Kluwer international series in engineering and computer science; Analog circuits and signal processing. Boston: Kluwer Academic. p. 21.ISBN 978-0-7923-9390-0.Channel length modulation in an MOS transistor causes the drain current to be dependent on the drain voltage.… and λ the channel-length modulation parameter.
^Li, Xue-Zhi; Yang, Junyuan; Martcheva, Maia (2020).Age Structured Epidemic Modeling. Interdisciplinary Applied Mathematics. Cham: Springer International Publishing AG. p. 7.ISBN 978-3-030-42495-4.λ* is called theMalthusian parameter orintrinsic growth rate.
^Tourlakis, George J. (2024).Discrete mathematics: a concise introduction. Synthesis lectures on mathematics & statistics. Cham: Springer. p. 37.ISBN 978-3-031-30487-3.The symbols prevalent in the literature used to denote the empty string are ϵ or λ. We will choose λ…
^International Phonetic Association (2021).Handbook of the International Phonetic Association: a guide to the use of the international phonetic alphabet (22. printing ed.). Cambridge: Cambridge University Press. p. 179.ISBN 978-0-521-63751-0.λ lambda voiceless dental or alveolar lateral fricativeNot IPA usage
^Bierens, Herman J. (2004).Introduction to the mathematical and statistical foundations of econometrics. Themes in modern econometrics. New York: Cambridge University Press. p. 19.ISBN 978-0-521-83431-5.This function λ is called the Lebesgue measure on⁠ $\mathbb {R}$ ⁠,...
^Leong, Frederick; Austin, James T. (2024).The psychology research handbook: a guide for graduate students and research assistants (Third ed.). Thousand Oaks London New Delhi Singapore: Sage. p. 280.ISBN 978-1-4522-1767-3.If the independent and dependent variables are nominal, the contingency coefficient, Cramer's V, or Goodman–Kruskal's λ may be chosen.
^Ribbens, William B. (2017).Understanding automotive electronics: an engineering perspective (8th ed.). Oxford: Elsevier/Butterworth-Heinemann, an imprint of Elsevier. p. 215.ISBN 978-0-12-810434-7.As a result, one of the most significant automotive engine sensors in use today is the exhaust gas oxygen (EGO) sensor. This sensor is often called alambda sensor from the Greek letter lambda (λ), which is commonly used to denote the equivalence ratio (as defined in chapter 4):
^"Encyclopedia Astronautica: Lambda".Astronautix.com. Archived fromthe original on 2012-10-22. Retrieved2012-12-18.
^Geng, Hwaiyu (2021).Data center handbook: plan, design, build, and operations of a smart data center (2nd ed.). Hoboken: Wiley. p. 278.ISBN 978-1-119-59753-7.Commonly, the failure rate is assumed to be constant and written as λ.
^Farrington, David; Kazemian, Lila; Piquero, Alex R., eds. (2019).The Oxford handbook of developmental and life-course criminology. The Oxford handbooks in criminology and criminal justice. New York: Oxford University Press. p. 74.ISBN 978-0-19-020137-1.In order to evaluate acceleration and deceleration in criminal activity over the life-course, it is first necessary to determine the individual crime rate, or lambda (λ), for each offender of interest.
^Wankat Separation Process Engineering 2nd ed, Prentice Hall
^"Half-Life on Steam".store.steampowered.com. Valve. Retrieved2017-01-02.
^"Half-Life 2 on Steam".store.steampowered.com. Valve. Retrieved2017-01-02.
^Rapp, Linda (2004)."Gay Activists Alliance"(PDF).glbtq.com.
^"1969, The Year of Gay Liberation".The New York Public Library. June 2009. Retrieved17 November 2018.
^Goodwin, Joseph P. (1989). "It Takes One to Know One".More Man Than You'll Ever Be: Gay Folklore and Acculturation in Middle America. Indiana University Press. p. 26.ISBN 978-0253338938.
^Rapp, Linda (2003)."Symbols"(PDF).glbtq.com.
^Haggerty, George E., ed. (2000).Gay Histories and Cultures: An Encyclopedia (Encyclopedia of Gay Histories and Cultures, Volume II) (1 ed.). London: Garland Publishing. p. 529.ISBN 0-8153-1880-4.OCLC 750790369.
^Weisstein, Eric W."Golomb-Dickman Constant Continued Fraction".mathworld.wolfram.com. Retrieved2025-01-31.
^Unicode Ancient Greek Numbers block.
^"Thesaurus Linguae Graecae"(PDF).Stephanus.TLG.UCI.edu. Archived fromthe original(PDF) on 2011-07-16.
^"Unicode Mail List Archive: RE: Greek letter "LAMDA"?".
^Humchitt, Robyn; Jacquerye, Denis; King, Kevin (2023-07-17)."L2/23-191: Proposal to Encode 3 Additional Latin Characters for Wakashan and Salishan Languages to the Unicode Standard"(PDF).
^"HTML 4.01 Specification. 24. Character entity references in HTML 4".World Wide Web Consortium.

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