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 w ...

, representing the

voiced alveolar lateral approximant The voiced alveolar lateral approximant is a type of consonantal sound used in many spoken languages. The symbol in the International Phonetic Alphabet that represents dental, alveolar, and postalveolar lateral approximants is , and the equ ...

. 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 tho ...

, lambda has a value of 30. Lambda is derived from the Phoenician

Lamed Lamedh or Lamed is the twelfth letter of the Semitic abjads, including Hebrew Lāmed , Aramaic Lāmadh , Syriac Lāmaḏ ܠ, Arabic , and Phoenician Lāmed . Its sound value is . The Phoenician letter gave rise to the Greek Lambda (Λ), Latin ...

. Lambda gave rise to the

Latin Latin (, or , ) is a classical language belonging to the 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 the power of the ...

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 peri ...

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 The history of the Greek alphabet starts with the adoption of Phoenician letter forms in the 9th–8th centuries BC during early Archaic Greece and continues to the present day. The Greek alphabet was developed during the Iron Age centuries af ...

, 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. NAMA Alphabet grec

Symbol

Upper-case letter Λ

Examples of the symbolic use of uppercase lambda include: * The

lambda particle The lambda baryons (Λ) are a family of subatomic hadron particles containing one up quark, one down quark, and a third quark from a higher flavour generation, in a combination where the quantum wave function changes sign upon the flavour of an ...

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 conta ...

of logical deduction in

first-order logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

. * There is a poetical allusion to the use of Lambda as a shield blazon by the

Spartans Sparta ( Doric Greek: Σπάρτα, ''Spártā''; Attic Greek: Σπάρτη, ''Spártē'') was a prominent city-state in Laconia, in ancient Greece. In antiquity, the city-state was known as Lacedaemon (, ), while the name Sparta referr ...

. * Lambda is the

von Mangoldt function In mathematics, the von Mangoldt function is an arithmetic function named after German mathematician Hans von Mangoldt. It is an example of an important arithmetic function that is neither multiplicative nor additive. Definition The von Mango ...

in mathematical

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...

. * Lambda denotes the de Bruijn–Newman constant which is closely connected with

Riemann's hypothesis In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in ...

. * In statistics, lambda is used for the

likelihood ratio The likelihood function (often simply called the likelihood) represents the probability of random variable realizations conditional on particular values of the statistical parameters. Thus, when evaluated on a given sample, the likelihood functi ...

. * In statistics, Wilks's lambda is used in multivariate analysis of variance (

MANOVA In statistics, multivariate analysis of variance (MANOVA) is a procedure for comparing multivariate sample means. As a multivariate procedure, it is used when there are two or more dependent variables, and is often followed by significance tests ...

analysis) to compare group means on a combination of dependent variables. * In the spectral decomposition of matrices, lambda indicates the

diagonal matrix In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal m ...

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'' (franchis ...

. * 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 practical disciplines (includi ...

, lambda is the time window over which a process is observed for determining the working memory set for a

digital computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These program ...

virtual memory In computing, virtual memory, or virtual storage is a memory management technique that provides an "idealized abstraction of the storage resources that are actually available on a given machine" which "creates the illusion to users of a very ...

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 A dwarf planet is a small planetary-mass object that is in direct orbit of the Sun, smaller than any of the eight classical planets but still a world in its own right. The prototypical dwarf planet is Pluto. The interest of dwarf planets to ...

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 Crystal optics is the branch of optics that describes the behaviour of light in ''anisotropic media'', that is, media (such as crystals) in which light behaves differently depending on which direction the light is propagating. The index of refract ...

, 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 No ...

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 ...

(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 outco ...

, 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 In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field eq ...

, a term added to some dynamical equations to account for the

accelerating expansion of the universe Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered duri ...

. * 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 characteristi ...

. 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 stud ...

, the lambda is the symbol of

Identitarianism The Identitarian movement or Identitarianism is a pan-European nationalist, far-right political ideology asserting the right of European ethnic groups and white peoples to Western culture and territories claimed to belong exclusively to them ...

, a

white nationalist White nationalism is a type of racial nationalism or pan-nationalism which espouses the belief that white people are a raceHeidi Beirich and Kevin Hicks. "Chapter 7: White nationalism in America". In Perry, Barbara. ''Hate Crimes''. Greenwoo ...

movement that originated in

France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of overseas regions and territories in the Americas and the Atlantic, Pacific and Indian Oceans. Its metropolitan area ...

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 subcontinent of Eurasia and it is located entirel ...

and later on to North America, Australia 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 count ...

. 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, t ...

of any

wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (re ...

, 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 r ...

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. * In

evolutionary algorithm In computational intelligence (CI), an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduct ...

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 In computer science, an evolution strategy (ES) is an optimization technique based on ideas of evolution. It belongs to the general class of evolutionary computation or artificial evolution methodologies. History The 'evolution strategy' optimizat ...

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 the ...

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 at ...

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 probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known co ...

. * 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 formal ...

and

, 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 denoted ...

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 matrices ...

. * 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 in ...

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 respe ...

(measured in coulombs per meter). * Lambda denotes a

Lagrange multiplier In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied e ...

in multi-dimensional calculus. * In

solid-state electronics Solid-state electronics means semiconductor electronics: electronic equipment using semiconductor devices such as transistors, diodes and integrated circuits (ICs). The term is also used as an adjective for devices in which semiconductor electr ...

, 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

. * In

formal language theory In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symb ...

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 cas ...

. * 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 The voiced alveolar lateral affricate is a type of consonantal sound, used in some spoken languages. The symbol in the International Phonetic Alphabet is (often simplified to ). Features Features of 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 concer ...

. * The

Goodman and Kruskal's lambda In probability theory and statistics, Goodman & Kruskal's lambda (\lambda) is a measure of proportional reduction in error in cross tabulation analysis. For any sample with a nominal independent variable and dependent variable (or ones that can be ...

in statistics 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 havin ...

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 Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...

of an

internal-combustion engine An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal combust ...

. * A

Lambda 4S The Lambda 4S or L-4S was an experimental Japanese expendable carrier rocket. It was produced by Nissan and the Institute of Space and Astronautical Science and launched five times between 1966 and 1970 with Ohsumi technology demonstration satell ...

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 specifi ...

, and it is measured in failure events per hour. Numerically, this lambda is also the reciprocal of the

mean time between failure Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a mechanical or electronic system during normal system operation. MTBF can be calculated as the arithmetic mean (average) time between failures of a system ...

s. * In criminology, lambda denotes an individual's frequency of offences. * In

, lambda also denotes the

ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...

ic conductance of a given ion (the composition of the ion is generally shown as a subscript to the lambda character). * In

neurobiology Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions and disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, developme ...

, 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 ( ...

along a length of a nerve cell's

axon An axon (from Greek ἄξων ''áxōn'', axis), or nerve fiber (or nerve fibre: see spelling differences), is a long, slender projection of a nerve cell, or neuron, in vertebrates, that typically conducts electrical impulses known as action p ...

. * 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 conduction, ...

, lambda denotes the heat of vaporization per

mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...

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 lette ...

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 pol ...

. * A block style lambda is used as a recurring symbol in the

Valve A valve is a device or natural object that regulates, directs or controls the flow of a fluid (gases, liquids, fluidized solids, or slurries) by opening, closing, or partially obstructing various passageways. Valves are technically fitting ...

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 at ...

'', 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 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 Alliance ...

. The lambda symbol became associated with

Gay Liberation The gay liberation movement was a social and political movement of the late 1960s through the mid-1980s that urged lesbians and gay men to engage in radical direct action, and to counter societal shame with gay pride.Hoffman, 2007, pp.xi-xiii ...

and recognized as an

LGBT symbol Over the course of its history, the LGBT community has adopted certain symbols for self-identification to demonstrate unity, pride, shared values, and allegiance to one another. These symbols communicate ideas, concepts, and identity both with ...

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 lette ...

''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 The iota subscript is a diacritic mark in the Greek alphabet shaped like a small vertical stroke or miniature iota placed below the letter. It can occur with the vowel letters eta , omega , and alpha . It represents the former presence of an o ...

(as λͅ). These are variously encoded in Unicode. The

Ancient Greek Numbers Ancient Greek Numbers is a Unicode block containing acrophonic numerals The Attic numerals are a symbolic number notation used by the ancient Greeks. They were also known as Herodianic numerals because they were first described in a 2nd- ...

Unicode block A Unicode block is one of several contiguous ranges of numeric character codes ( code points) of the Unicode character set that are defined by the Unicode Consortium for administrative and documentation purposes. Typically, proposals such as the ...

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.

References

{{Reflist Greek letters LGBT symbols

Symbol

Upper-case letter Λ

Lower-case letter λ

Litra symbol

Character encodings

See also

References