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Lambda (}, ''lám(b)da'') is the 11th letter of the
Greek alphabet The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as ...
, representing the voiced alveolar lateral approximant . In the system of
Greek numerals Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those ...
, lambda has a value of 30. Lambda is derived from the Phoenician Lamed . Lambda gave rise to the
Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
L and the Cyrillic El (Л). The ancient grammarians and dramatists give evidence to the pronunciation as () in
Classical Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic pe ...
times. In
Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the dialects of the Greek language spoken in the modern era, including the official standardized form of the ...
, the name of the letter, Λάμδα, is pronounced . In early Greek alphabets, the shape and orientation of lambda varied. 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 the Ionic alphabet, Greek settled on an angle at the top; the Romans put the angle at the lower-left. The HTML 4 character entity references for the Greek capital and small letter lambda are Λ and λ respectively. The Unicode code points for lambda are U+039B and U+03BB.


Symbol


Upper-case letter Λ

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 In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contai ...
of logical deduction in first-order logic. * There is a poetical allusion to the use of Lambda as a shield blazon by the Spartans. * Lambda is the von Mangoldt function in mathematical number theory. * Lambda denotes the de Bruijn–Newman constant which is closely connected with Riemann's hypothesis. * In
statistics Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, indust ...
, 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. * In the spectral decomposition of matrices, lambda indicates the diagonal matrix of the eigenvalues of the
matrix Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** '' The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchi ...
. * In
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
, 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 A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
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. * In crystal optics, lambda is used to represent a lattice period. * In
NATO The North Atlantic Treaty Organization (NATO, ; french: Organisation du traité de l'Atlantique nord, ), also called the North Atlantic Alliance, is an intergovernmental military alliance between 30 member states – 28 European and two N ...
military operations, a
chevron Chevron (often relating to V-shaped patterns) may refer to: Science and technology * Chevron (aerospace), sawtooth patterns on some jet engines * Chevron (anatomy), a bone * '' Eulithis testata'', a moth * Chevron (geology), a fold in rock la ...
(a heraldic symbol which looks like a capital letter lambda or inverted V) is painted on the vehicles of this military alliance for identification. * In
electrochemistry Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an out ...
, lambda denotes the "equivalent conductance" of an electrolyte solution. * In
cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
, lambda is the symbol for the cosmological constant, a term added to some dynamical equations to account for the accelerating expansion of the universe. * In optics, lambda denotes the grating pitch of a
Bragg reflector A distributed Bragg reflector (DBR) is a reflector used in waveguides, such as optical fibers. It is a structure formed from multiple layers of alternating materials with varying refractive index, or by periodic variation of some characterist ...
. Also in optics, it denotes wavelength of light. * In
politics Politics (from , ) is the set of activities that are associated with making decisions in groups, or other forms of power relations among individuals, such as the distribution of resources or status. The branch of social science that studies ...
, the lambda is the symbol of Identitarianism, a white nationalist movement that originated in
France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...
before spreading out to the rest of
Europe Europe is a large peninsula conventionally considered a continent in its own right because of its great physical size and the weight of its history and traditions. Europe is also considered a Continent#Subcontinents, subcontinent of Eurasia ...
and later on to
North America North America is a continent in the Northern Hemisphere and almost entirely within the Western Hemisphere. It is bordered to the north by the Arctic Ocean, to the east by the Atlantic Ocean, to the southeast by South America and th ...
,
Australia Australia, officially the Commonwealth of Australia, is a sovereign country comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands. With an area of , Australia is the largest country by ...
and
New Zealand New Zealand ( mi, Aotearoa ) is an island country in the southwestern Pacific Ocean. It consists of two main landmasses—the North Island () and the South Island ()—and over 700 smaller islands. It is the sixth-largest island coun ...
. The Identitarian lambda represents the Battle of Thermopylae.


Lower-case letter λ

Examples of the symbolic use of lowercase lambda include: * Lambda indicates the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
of any wave, especially in
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
,
electronic engineering Electronics engineering is a sub-discipline of electrical engineering which emerged in the early 20th century and is distinguished by the additional use of active components such as semiconductor devices to amplify and control electric current ...
, and
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
. * 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. * Lambda indicates the radioactivity decay constant in
nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies t ...
and radioactivity. This constant is very simply related (by a multiplicative constant) to the
half-life Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ...
of any radioactive material. * In
probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...
, lambda represents the density of occurrences within a time interval, as modelled by the Poisson distribution. * In
mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of forma ...
and
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
, lambda is used to introduce anonymous functions expressed with the concepts of lambda calculus. * Lambda indicates an
eigenvalue In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denote ...
in the mathematics of
linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrice ...
. * In the physics of electric fields, lambda sometimes indicates the linear
charge density In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system i ...
of a uniform line of
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons res ...
(measured in coulombs per meter). * Lambda denotes a Lagrange multiplier in multi-dimensional calculus. * In solid-state electronics, lambda indicates the
channel length modulation Channel length modulation (CLM) is an effect in field effect transistors, a shortening of the length of the inverted channel region with increase in drain bias for large drain biases. The result of CLM is an increase in current with drain bias an ...
parameter of a MOSFET. * In
ecology Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overl ...
, lambda denotes the long-term intrinsic growth rate of a population. This value is often calculated as the dominant eigenvalue of the age/size class
matrix Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** '' The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchi ...
. * In formal language theory and in computer science, lambda denotes the
empty string In formal language theory, the empty string, or empty word, is the unique string of length zero. Formal theory Formally, a string is a finite, ordered sequence of characters such as letters, digits or spaces. The empty string is the special c ...
. * Lambda is a nonstandard symbol in the
International Phonetic Alphabet The International Phonetic Alphabet (IPA) is an alphabetic system of phonetic notation based primarily on the Latin script. It was devised by the International Phonetic Association in the late 19th century as a standardized representation ...
for the voiced alveolar lateral affricate . * Lambda denotes the Lebesgue measure in
mathematical set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...
. * The Goodman and Kruskal's lambda in
statistics Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, indust ...
indicates the
proportional reduction in error Proportional reduction in loss (PRL) is a general framework for developing and evaluating measures of the reliability of particular ways of making observations which are possibly subject to errors of all types. Such measures quantify how much havi ...
when one variable's values are used to predict the values of another variable. * Lambda denotes the oxygen sensor in a vehicle that measures the air-to-fuel ratio in the exhaust gases of an internal-combustion engine. * A Lambda 4S solid-fuel rocket was used to launch Japan's first orbital satellite in 1970. * Lambda denotes the failure rate of devices and systems in
reliability theory Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specifie ...
, and it is measured in failure events per hour. Numerically, this lambda is also the reciprocal of the mean time between failures. * In criminology, lambda denotes an individual's frequency of offences. * In
electrochemistry Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an out ...
, 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 The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...
across the
cell membrane The cell membrane (also known as the plasma membrane (PM) or cytoplasmic membrane, and historically referred to as the plasmalemma) is a biological membrane that separates and protects the interior of all cells from the outside environment (t ...
along a length of a nerve cell's axon. * In the science and technology of
heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy ( heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conducti ...
, lambda denotes the heat of vaporization per mole of material (a.k.a. its "latent heat"). * In the technology and science of celestial navigation, lambda denotes the
longitude Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek let ...
as opposed to the Roman letter "L", which denotes the
latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north ...
. * A block style lambda is used as a recurring symbol in the Valve computer game series ''
Half-Life Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ...
'', referring to the Lambda complex of the fictional
Black Mesa Research Facility The Black Mesa Research Facility (also simply called Black Mesa) is a fictional underground laboratory complex that serves as the primary setting for the video game ''Half-Life'' and its expansions, as well as its remake, '' Black Mesa''. It als ...
, as well as making appearances in the sequel ''Half-Life 2'', and its subsequent prequel ''Half-Life: Alyx'' as an in universe logo. * In 1970, a lowercase lambda was chosen by
Tom Doerr Thomas L. Doerr (1947 – August 2, 1987) was an American gay activist. In 1970, he introduced the lambda symbol into the gay rights movement when the image was used to represent the political work of the Gay Activists Alliance. The lambda became " ...
as the symbol of the New York chapter of the
Gay Activists Alliance The Gay Activists Alliance (GAA) was founded in New York City on December 21, 1969, almost six months after the Stonewall riots, by dissident members of the Gay Liberation Front (GLF). In contrast to the Liberation Front, the Activists Allianc ...
. The lambda symbol became associated with Gay Liberation and recognized as an LGBT symbol for some time afterwards, being used as such by the International Gay Rights Congress in Edinburgh.


Litra symbol

The
Roman Roman or Romans most often refers to: * Rome, the capital city of Italy * Ancient Rome, Roman civilization from 8th century BC to 5th century AD *Roman people, the people of ancient Rome *''Epistle to the Romans'', shortened to ''Romans'', a lett ...
''libra'' and
Byzantine The Byzantine Empire, also referred to as the Eastern Roman Empire or Byzantium, was the continuation of the Roman Empire primarily in its eastern provinces during Late Antiquity and the Middle Ages, when its capital city was Constantinopl ...
''lítra'' (), 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 (as λͅ). These are variously encoded in Unicode. The Ancient Greek Numbers Unicode block includes 10183 (𐆃) as well as 𐅢, which is described as 10162 but was much more common as a form of the litra sign. A variant of the sign can be formed from 0338 and either 039B (Λ̸) or 03BB (λ̸).


Character encodings

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". * Greek Lambda / Coptic Laula * Mathematical Lambda These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.


See also

*
Barred lambda The barred lambda ƛ, (in Unicode ), also called running man,
(strictly speaking, this refers to the El (Cyrillic) – Л, л * Fraser alphabet#Consonants * Greek letters used in mathematics, science, and engineering


References

{{Reflist Greek letters LGBT symbols