Editing Lambda (section)

==Symbol==
===Upper-case letter Λ===
Examples of the symbolic use of uppercase lambda include:
* The [[lambda particle]] is a type of [[subatomic particle]] in [[Physics#High energy/particle physics|subatomic particle physics]].
* Lambda is the set of logical axioms in the [[axiomatic method]] of logical deduction in [[first-order logic]].
* There is a poetical allusion to the use of Lambda as a [[aspis|shield blazon]] by the [[Spartans]].{{Citation needed|date=March 2022}}<ref>{{cite book |last1=Philodemus |title=On Poems |date=2003 |publisher=Oxford University Press |page=212 |isbn=9780199262854}}</ref>
* Lambda is the [[von Mangoldt function]] in mathematical [[number theory]].<ref>{{Cite book |last=Deza |first=Elena |title=Perfect and amicable numbers |date=2023 |publisher=World Scientific |isbn=978-981-12-5962-3 |series=Selected chapters of number theory : special numbers |location=New Jersey |pages=79 |quote=The ''von Mangold function'' Λ(''n'') is defined as…}}</ref>
* Lambda denotes the [[de Bruijn–Newman constant]] which is closely connected with [[Riemann's hypothesis]].<ref>{{Cite book |last=Broughan |first=Kevin A. |title=Equivalents of the Riemann hypothesis. Volume 3: Further steps towards resolving the Riemann hypothesis / Kevin Broughan (University of Waikato, New Zealand) |date=2024 |publisher=Cambridge University Press |isbn=978-1-009-38480-3 |series=Encyclopedia of mathematics and its applications |location=Cambridge, UK; New York; Port Melbourne, Victoria; New Delhi; Singapore |pages=63 |quote=Now we can give the definition of the de Bruijn–Newman constant Λ.}}</ref>
* In [[statistics]], lambda is used for the [[Likelihood function#Likelihood ratio|likelihood ratio]].
* In statistics, [[Samuel Stanley Wilks|Wilks's lambda]] is used in multivariate analysis of variance ([[MANOVA]] analysis) to compare group means on a combination of dependent variables.<ref>{{Cite book |last=Everitt |first=Brian |title=An introduction to applied multivariate analysis with R |date=2011 |publisher=Springer New York |others=Torsten Hothorn |isbn=978-1-4419-9649-7 |series=Use R! Ser |location=New York |quote=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):}}</ref>
* In the [[Eigendecomposition of a matrix#Normal matrices|spectral decomposition of matrices]], lambda indicates the [[diagonal matrix]] of the [[eigenvalues]] of the [[Matrix (mathematics)|matrix]].
* In [[computer science]], lambda is the time window over which a process is observed for determining the working memory set for a [[digital computer]]'s [[virtual memory]] management.
* In [[astrophysics]], lambda represents the likelihood that a small body will encounter a [[planet]] or a [[dwarf planet]] leading to a deflection of a significant magnitude. An object with a large value of lambda is expected to have [[Clearing the neighbourhood|cleared its neighbourhood]], satisfying the current [[definition of planet|definition of a planet]].<ref>{{Cite book |last=Wilkinson |first=John |title=The Solar System in Close-Up |date=2016 |publisher=Springer International Publishing AG |isbn=978-3-319-27627-4 |series=Astronomers' Universe Ser |location=Cham |pages=7 |quote=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".}}</ref>
* In [[crystal optics]], lambda is used to represent a lattice period.
* In [[electrochemistry]], lambda denotes the "equivalent [[Electrical conductance|conductance]]" of an [[electrolyte]] solution.<ref>{{Cite book |last=Kuhn |first=Reinhard |title=Capillary electrophoresis: principles and practice |last2=Hoffstetter-Kuhn |first2=Sabrina |date=1993 |publisher=Springer |isbn=978-0-387-56434-0 |series=Springer Laboratory |location=Berlin Heidelberg |pages=12 |quote=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…}}</ref>
* In [[cosmology]], lambda is the symbol for the [[cosmological constant]], a term added to some dynamical equations to account for the [[accelerating expansion of the universe]].<ref>{{Cite book |last=Liddle |first=Andrew R. |title=An introduction to modern cosmology |date=2015 |publisher=John Wiley and Sons, Inc |isbn=978-1-118-50214-3 |edition=Third |location=Chichester, West Sussex |pages=55 |quote=The cosmological constant Λ appears in the Friedman equation as an extra term,}}</ref>
* In optics, lambda denotes the grating pitch of a [[Bragg reflector]].<ref>{{Cite book |title=Frontiers in Guided Wave Optics and Optoelectronics |date=2010 |publisher=IntechOpen |isbn=978-953-7619-82-4 |editor-last=Pal |editor-first=Bishnu |location=Erscheinungsort nicht ermittelbar |pages=352 |quote=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.}}</ref>
* In [[politics]], the lambda is the symbol of [[Identitarian movement|Identitarianism]], a [[white nationalist]] movement that originated in [[France]] before spreading out to the rest of [[Europe]] and later on to [[North America]], [[Australia]] and [[New Zealand]]. The Identitarian lambda represents the [[Battle of Thermopylae]].

===Lower-case letter λ===
[[File:Greek lc lamda thin.svg|thumb|upright=0.5|Lower-case lambda]]

Examples of the symbolic use of lowercase lambda include:
* λ indicates the [[wavelength]] of any [[wave]], especially in [[physics]], [[electrical engineering]], and [[mathematics]].<ref>{{Cite book |title=Fundamentals of Physics |last=Nelkon |first=Michael |publisher=Hart-Davis Educational |year=1977 |location=St. Albans, Hertfordshire |pages=329}}</ref>
* In [[evolutionary algorithm]]s, λ indicates the number of offspring that would be generated from μ current population in each generation. The terms μ and λ are originated from [[Evolution strategy]] notation.<ref>{{Cite book |last=Baragona |first=Roberto |title=Evolutionary statistical procedures: an evolutionary computation approach to statistical procedures designs and applications |date=2011 |publisher=Springer |others=Francesco Battaglia, Irene Poli |isbn=978-3-642-16217-6 |series=Statistics and computing |location=Berlin |pages=16 |quote=… ,and λ is the number of offsprings at each generation:}}</ref>
* λ indicates the [[exponential decay|radioactivity decay constant]] in [[nuclear physics]] and [[radioactivity]]. This constant is very simply related (by a multiplicative constant) to the [[half-life]] of any radioactive material.
* In [[probability theory]], λ represents the density of occurrences within a time interval, as modelled by the [[Poisson distribution]].<ref>{{Cite book |last=Panik |first=Michael J. |title=Advanced statistics from an elementary point of view |date=2005 |publisher=Elsevier/Academic Press |isbn=978-0-12-088494-0 |location=Boston |pages=260 |quote=Since λ is the mean number of occurrences per unit time of the Poisson process,}}</ref>
* In [[mathematical logic]] and [[computer science]], λ is used to introduce [[anonymous function]]s expressed with the concepts of [[lambda calculus]].
* λ indicates an [[eigenvalue]] in the mathematics of [[linear algebra]].
* In the physics of particles, lambda indicates the [[thermal de Broglie wavelength]]<ref>{{Cite book |last=Tabatabaian |first=Mehrzad |title=Advanced thermodynamics: fundamentals, mathematics, applications |last2=Rajput |first2=R. K. |date=2018 |publisher=Mercury Learning and Information |isbn=978-1-936420-27-8 |location=Dulles, Virginia Boston, Massachusetts New Delhi |pages=434 |quote=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,…}}</ref>
* In the physics of [[electric field]]s, lambda sometimes indicates the linear [[charge density]] of a uniform line of [[electric charge]] (measured in [[coulomb]]s per meter).
* Lambda denotes a [[Lagrange multiplier]] in [[multivariable calculus|multi-dimensional calculus]].<ref>{{Cite book |last=Ito |first=Kazufumi |title=Lagrange multiplier approach to variational problems and applications |date=2008 |publisher=Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, Pennsylvania 19104) |others=K. Kunisch, Society for Industrial and Applied Mathematics |isbn=978-0-89871-649-8 |series=Advances in Design and Control |location=Philadelphia, Pa |pages=xii |quote=Here the Lagrange multiplier λ is treated like an independent variable just like ''y'' and ''u''.}}</ref>
* In [[solid-state electronics]], lambda indicates the [[channel length modulation]] parameter of a [[MOSFET]].<ref>{{Cite book |last=Wiegerink |first=Remco J. |title=Analysis and synthesis of MOS translinear circuits |date=1993 |publisher=Kluwer Academic |isbn=978-0-7923-9390-0 |series=The Kluwer international series in engineering and computer science ; Analog circuits and signal processing |location=Boston |pages=21 |quote=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.}}</ref>
* In [[ecology]], lambda denotes the long-term intrinsic growth rate of a population.<ref>{{Cite book |last=Li |first=Xue-Zhi |title=Age Structured Epidemic Modeling |last2=Yang |first2=Junyuan |last3=Martcheva |first3=Maia |date=2020 |publisher=Springer International Publishing AG |isbn=978-3-030-42495-4 |series=Interdisciplinary Applied Mathematics |location=Cham |pages=7 |quote=λ* is called the ''Malthusian parameter'' or ''intrinsic growth rate''.}}</ref> This value is often calculated as the dominant eigenvalue of the age/size class [[matrix (mathematics)|matrix]].
* In [[formal language theory]] and in computer science, lambda denotes the [[empty string]].<ref>{{Cite book |last=Tourlakis |first=George J. |title=Discrete mathematics: a concise introduction |date=2024 |publisher=Springer |isbn=978-3-031-30487-3 |series=Synthesis lectures on mathematics & statistics |location=Cham |pages=37 |quote=The symbols prevalent in the literature used to denote the empty string are ϵ or λ. We will choose λ…}}</ref>
* Lambda is a nonstandard symbol in the [[Obsolete and nonstandard symbols in the International Phonetic Alphabet|International Phonetic Alphabet]] for the [[voiced alveolar lateral affricate]] {{IPAblink|dɮ}}.<ref>{{Cite book |last=International Phonetic Association |title=Handbook of the International Phonetic Association: a guide to the use of the international phonetic alphabet |date=2021 |publisher=Cambridge University Press |isbn=978-0-521-63751-0 |edition=22. printing |location=Cambridge |pages=179 |quote=λ  lambda  voiceless dental or alveolar lateral fricative ''Not IPA usage''}}</ref>
* Lambda denotes the [[Lebesgue measure]] in [[Set theory|mathematical set theory]].<ref>{{Cite book |last=Bierens |first=Herman J. |title=Introduction to the mathematical and statistical foundations of econometrics |date=2004 |publisher=Cambridge University Press |isbn=978-0-521-83431-5 |series=Themes in modern econometrics |location=New York |pages=19 |quote=This function λ is called the Lebesgue measure on  {{tmath|\R}},...}}</ref>
* The [[Goodman and Kruskal's lambda]] in [[statistics]] indicates the [[proportional reduction in error]] when one variable's values are used to predict the values of another variable.<ref>{{Cite book |last=Leong |first=Frederick |title=The psychology research handbook: a guide for graduate students and research assistants |last2=Austin |first2=James T. |date=2024 |publisher=Sage |isbn=978-1-4522-1767-3 |edition=Third |location=Thousand Oaks London New Delhi Singapore |pages=280 |quote=If the independent and dependent variables are nominal, the contingency coefficient, Cramer's V, or Goodman–Kruskal's λ may be chosen.}}</ref>
* Lambda denotes the [[oxygen sensor]] in a vehicle that measures the [[air-fuel ratio|air-to-fuel ratio]] in the exhaust [[gases]] of an [[internal-combustion engine]].<ref>{{Cite book |last=Ribbens |first=William B. |title=Understanding automotive electronics: an engineering perspective |date=2017 |publisher=Elsevier/Butterworth-Heinemann, an imprint of Elsevier |isbn=978-0-12-810434-7 |edition=8th |location=Oxford |pages=215 |quote=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 a ''lambda sensor'' from the Greek letter lambda (λ), which is commonly used to denote the equivalence ratio (as defined in chapter 4):}}</ref>
* A [[Lambda (rocket)|Lambda 4S]] solid-fuel rocket was used to launch [[Ohsumi (satellite)|Japan's first orbital satellite]] in 1970.<ref>{{cite web |url=http://www.astronautix.com/lvs/lambda.htm |title=Encyclopedia Astronautica: Lambda |website=Astronautix.com |access-date=2012-12-18 |url-status=dead |archive-url=https://web.archive.org/web/20121022140407/http://www.astronautix.com/lvs/lambda.htm |archive-date=2012-10-22}}</ref>
* Lambda denotes the [[failure rate]] of devices and systems in [[reliability theory]], and it is measured in failure events per hour. Numerically, this lambda is also the reciprocal of the [[mean time between failure]]s.<ref>{{Cite book |last=Geng |first=Hwaiyu |title=Data center handbook: plan, design, build, and operations of a smart data center |date=2021 |publisher=Wiley |isbn=978-1-119-59753-7 |edition=2nd |location=Hoboken |pages=278 |quote=Commonly, the failure rate is assumed to be constant and written as λ.}}</ref>
* In criminology, lambda denotes an individual's frequency of [[Offence (law)|offences]].<ref>{{Cite book |title=The Oxford handbook of developmental and life-course criminology |date=2019 |publisher=Oxford University Press |isbn=978-0-19-020137-1 |editor-last=Farrington |editor-first=David |series=The Oxford handbooks in criminology and criminal justice |location=New York |pages=74 |quote=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. |editor-last2=Kazemian |editor-first2=Lila |editor-last3=Piquero |editor-first3=Alex R.}}</ref>
* In [[electrochemistry]], lambda also denotes the [[ion]]ic conductance of a given ion (the composition of the ion is generally shown as a subscript to the lambda character).
* In [[neurobiology]], lambda denotes the [[length constant]] (or exponential rate of decay) of the [[electric potential]] across the [[cell membrane]] along a length of a nerve cell's [[axon]].
* In the science and technology of [[heat transfer]], lambda denotes the [[heat of vaporization]] per [[Mole (unit)|mole]] of material (a.k.a. its "latent heat").<ref>Wankat Separation Process Engineering 2nd ed, Prentice Hall</ref>
* In the technology and science of [[celestial navigation]], lambda denotes the [[longitude]] as opposed to the Roman letter "L", which denotes the [[latitude]].
* A block style lambda is used as a recurring symbol in the [[Valve Corporation|Valve]] computer game series ''[[Half-Life (series)|Half-Life]]'',<ref>{{cite web |title=Half-Life on Steam |url=http://store.steampowered.com/app/70/ |website=store.steampowered.com |publisher=Valve |access-date=2017-01-02}}</ref> referring to the Lambda Complex of the fictional [[Black Mesa Research Facility]], as well as making appearances in the sequel ''[[Half-Life 2]]'', and its subsequent prequel ''[[Half-Life: Alyx]]'' as an in-universe [[Political symbolism|symbol of resistance]].<ref>{{cite web |title=Half-Life 2 on Steam |url=http://store.steampowered.com/app/220/ |website=store.steampowered.com |publisher=Valve |access-date=2017-01-02}}</ref>
* In 1970, a lowercase lambda was chosen by [[Tom Doerr]] as the symbol of the New York chapter of the [[Gay Activists Alliance]].<ref>{{cite web |last=Rapp |first=Linda |title=Gay Activists Alliance |url=http://www.glbtqarchive.com/ssh/gay_activists_alliance_S.pdf |publisher=[[glbtq.com]] |year=2004}}</ref><ref>{{cite web |title=1969, The Year of Gay Liberation |url=http://web-static.nypl.org/exhibitions/1969/ref/1696848.html |publisher=[[The New York Public Library]] |date=June 2009 |access-date=17 November 2018}}</ref> The lambda symbol became associated with [[gay liberation]]<ref>{{cite book |last1=Goodwin |first1=Joseph P. |title=More Man Than You'll Ever Be: Gay Folklore and Acculturation in Middle America |url=https://archive.org/details/moremanthanyoull00good |url-access=registration |date=1989 |publisher=Indiana University Press |page=[https://archive.org/details/moremanthanyoull00good/page/26 26] |chapter=It Takes One to Know One |isbn=978-0253338938}}</ref><ref>{{cite web |last1=Rapp |first1=Linda |title=Symbols |url=http://www.glbtqarchive.com/arts/symbols_A.pdf |publisher=[[glbtq.com]] |date=2003}}</ref> and recognized as an [[LGBTQ symbols|LGBTQ symbol]] for some time afterwards, being used as such by the International Gay Rights Congress in Edinburgh.<ref>{{cite book |editor1-last=Haggerty |editor1-first=George E. |title=Gay Histories and Cultures: An Encyclopedia (Encyclopedia of Gay Histories and Cultures, Volume II) |date=2000 |publisher=Garland Publishing |location=London |page=[https://archive.org/details/encyclopediaofga00ghag/page/529 529] |edition=1 |oclc=750790369 |isbn=0-8153-1880-4 |url-access=registration |url=https://archive.org/details/encyclopediaofga00ghag/page/529 }}</ref>
* [[Golomb–Dickman constant]]<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Golomb-Dickman Constant Continued Fraction |url=https://mathworld.wolfram.com/Golomb-DickmanConstantContinuedFraction.html |access-date=2025-01-31 |website=mathworld.wolfram.com |language=en}}</ref>

===Litra symbol===
The [[Roman units|Roman]] {{lang|la|libra}} and [[Byzantine units|Byzantine]] {{lang|grc-x-medieval|lítra}} ({{lang|grc-x-medieval|λίτρα}}), which served as both the pound mass unit and liter volume unit, were abbreviated in Greek using lambda with modified forms of the [[iota subscript]] ⟨λͅ⟩. These are variously encoded in Unicode. The [[Ancient Greek Numbers (Unicode block)|Ancient Greek Numbers]] [[Unicode block]] includes 10183 {{sc|greek litra sign}} (𐆃) as well as 𐅢, which is described as 10162 {{sc|greek acrophonic hermionian ten}}<ref>[https://www.unicode.org/charts/PDF/U10140.pdf Unicode Ancient Greek Numbers block].</ref> but was much more common as a form of the litra sign. A variant of the sign can be formed from 0338 {{sc|combining long solidus overlay}} and either 039B {{sc|greek capital letter lamda}} (Λ̸) or 03BB {{sc|greek small letter lamda}} (λ̸).<ref>{{cite web |url=http://stephanus.tlg.uci.edu/encoding/BCM2010.pdf|archive-url=https://web.archive.org/web/20110716030016/http://stephanus.tlg.uci.edu/encoding/BCM2010.pdf |url-status=dead |archive-date=2011-07-16 |title=Thesaurus Linguae Graecae |website=Stephanus.TLG.UCI.edu }}</ref>