Lambda

Examples of the symbolic use of uppercase lambda include:

• The lambda particle is a type of subatomic particle in 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 shield blazon by the Spartans.{{Citation needed|date=March 2022}}{{cite book |last1=Philodemus |title=On Poems |date=2003 |publisher=Oxford University Press |page=212 |isbn=9780199262854}}
• Lambda is the von Mangoldt function in mathematical number theory.{{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…}}
• Lambda denotes the de Bruijn–Newman constant which is closely connected with Riemann's hypothesis.{{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, United Kingdom New York, NY, USA Port Melbourne, VIC, Australia New Delhi, India Singapore |pages=63 |quote=Now we can give the definition of the de Bruijn–Newman constant Λ.}}
• In statistics, lambda is used for the likelihood 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.{{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, NY |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):}}
• In the spectral decomposition of matrices, lambda indicates the diagonal matrix of the eigenvalues of the 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 cleared its neighbourhood, satisfying the current definition of a planet.{{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".}}
• In crystal optics, lambda is used to represent a lattice period.
• In electrochemistry, lambda denotes the "equivalent conductance" of an electrolyte solution.{{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…}}
• 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.{{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,}}
• In optics, lambda denotes the grating pitch of a Bragg reflector.{{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.}}
• In politics, the lambda is the symbol of 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.

File:Greek lc lamda thin.svg

Examples of the symbolic use of lowercase lambda include:

• λ indicates the wavelength of any wave, especially in physics, electrical engineering, and mathematics.{{Cite book |title=Fundamentals of Physics |last=Nelkon |first=Michael |publisher=Hart-Davis Educational |year=1977 |location=St. Albans, Hertfordshire |pages=329}}
• In evolutionary 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 from Evolution strategy notation.{{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:}}
• λ indicates the 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.{{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,}}
• In mathematical logic and computer science, λ is used to introduce anonymous functions 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{{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,…}}
• In the physics of electric fields, lambda sometimes indicates the linear charge density of a uniform line of electric charge (measured in coulombs per meter).
• Lambda denotes a Lagrange multiplier in multi-dimensional calculus.{{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, PA 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.}}
• In solid-state electronics, lambda indicates the channel length modulation parameter of a MOSFET.{{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.}}
• In ecology, lambda denotes the long-term intrinsic growth rate of a population.{{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.}} This value is often calculated as the dominant eigenvalue of the age/size class matrix.
• In formal language theory and in computer science, lambda denotes the empty string.{{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…}}
• Lambda is a nonstandard symbol in the International Phonetic Alphabet for the voiced alveolar lateral affricate {{IPAblink|dɮ}}.{{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}}
• Lambda denotes the Lebesgue measure in mathematical set theory.{{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}},...}}
• 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.{{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.}}
• Lambda denotes the oxygen sensor in a vehicle that measures the air-to-fuel ratio in the exhaust gases of an internal-combustion engine.{{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):}}
• A Lambda 4S solid-fuel rocket was used to launch Japan's first orbital satellite in 1970.{{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}}
• 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 failures.{{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.}}
• In criminology, lambda denotes an individual's frequency of offences.{{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, NY |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.}}
• In electrochemistry, lambda also denotes the ionic 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 of material (a.k.a. its "latent heat").Wankat Separation Process Engineering 2nd ed, Prentice Hall
• 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 computer game series Half-Life,{{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}} 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 symbol of resistance.{{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}}
• In 1970, a lowercase lambda was chosen by Tom Doerr as the symbol of the New York chapter of the Gay Activists Alliance.{{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}}{{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}} The lambda symbol became associated with gay liberation{{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}}{{cite web |last1=Rapp |first1=Linda |title=Symbols |url=http://www.glbtqarchive.com/arts/symbols_A.pdf |publisher=glbtq.com |date=2003}} and recognized as an LGBTQ symbol for some time afterwards, being used as such by the International Gay Rights Congress in Edinburgh.{{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 }}
• Golomb–Dickman constant{{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}}

The lambda has been a staple with the Half-Life franchise. The logo of the original game included the lambda, (e.g.: Hλlf-Life) and has since branched out into the gameplay itself with the release of Half-Life 2, being that having a lambda on the wall indicates to the player that there is a secret nearby.

The Roman {{lang|la|libra}} and 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 includes 10183 {{sc|greek litra sign}} (𐆃) as well as 𐅢, which is described as 10162 {{sc|greek acrophonic hermionian ten}}[https://www.unicode.org/charts/PDF/U10140.pdf Unicode Ancient Greek Numbers block]. 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).{{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 }}

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".{{Cite web|url=https://www.unicode.org/mail-arch/unicode-ml/y2010-m06/0063.html|title = Unicode Mail List Archive: RE: Greek letter "LAMDA"?}} Latin versions of lambda were added to Unicode in 2024 for the Salishan and Wakashan languages in Canada.{{cite web|title=L2/23-191: Proposal to Encode 3 Additional Latin Characters for Wakashan and Salishan Languages to the Unicode Standard|date=2023-07-17|url=https://www.unicode.org/L2/L2023/23191-three-latin-additions.pdf|first1=Robyn|last1=Humchitt|first2=Denis|last2=Jacquerye|first3=Kevin|last3=King}}

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• {{unichar|03BB|html=}}
• {{unichar|1D27|html=}}
• {{unichar|2C96|html=}}
• {{unichar|2C97|html=}}
• {{unichar|A7DA}}
• {{unichar|A7DB}}
• {{unichar|1038D}}
• {{unichar|1D6B2}}{{efn|The {{sc|mathematical}} 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.}}
• {{unichar|1D6CC}}
• {{unichar|1D6EC}}
• {{unichar|1D706}}
• {{unichar|1D726}}
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• {{unichar|1D760}}
• {{unichar|1D77A}}
• {{unichar|1D79A}}
• {{unichar|1D7B4}}

{{notelist}}

{{Wiktionary|Λ|λ}}

• Barred lambda - ƛ
• El (Cyrillic) – Л, л
• Fraser alphabet#Consonants
• Greek letters used in mathematics, science, and engineering

{{Reflist}}

Category:Greek letters

Category:LGBTQ symbols