Lambda (}, ''lám(b)da'') is the 11th letter of the Greek alphabet, representing the voiced alveolar lateral approximant . In the system of Greek numerals, lambda has a value of 30. Lambda is derived from the Phoenician Lamed Phoenician lamedh

. Lambda gave rise to the Latin L and the

Cyrillic , bg, кирилица , mk, кирилица , russian: кириллица , sr, ћирилица, uk, кирилиця , fam1 = Egyptian hieroglyphs , fam2 = Proto-Sinaitic , fam3 = Phoenician , fam4 = G ...

El (Л). The ancient grammarians and dramatists give evidence to the pronunciation as () in Classical Greek times. In Modern Greek, 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. NAMA Alphabet grec

Symbol

Upper-case letter Λ

Examples of the symbolic use of uppercase lambda include: * The lambda particle is a type of

subatomic particle In physical sciences, a subatomic particle is a particle that composes an atom. According to the Standard Model of particle physics, a subatomic particle can be either a composite particle, which is composed of other particles (for example, a pr ...

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 contains ...

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 The de Bruijn–Newman constant, denoted by Λ and named after Nicolaas Govert de Bruijn and Charles M. Newman, is a mathematical constant defined via the zero of a function, zeros of a certain function (mathematics), function ''H''(''λ'', ...

which is closely connected with Riemann's hypothesis. * In

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, 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 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 b ...

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, 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 Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the h ...

, 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 The definition of ''planet'', since the word was coined by the ancient Greeks, has included within its scope a wide range of celestial bodies. Greek astronomy, Greek astronomers employed the term (), 'wandering stars', for star-like objects wh ...

. * In crystal optics, lambda is used to represent a lattice period. * In NATO military operations, a chevron (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, lambda denotes the "equivalent conductance" of an

electrolyte An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon dis ...

solution. * 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. * 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, 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 movement that originated in France before spreading out to the rest of Europe 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 the Car ...

Australia Australia, officially the Commonwealth of Australia, is a Sovereign state, sovereign country comprising the mainland of the Australia (continent), Australian continent, the island of Tasmania, and numerous List of islands of Australia, sma ...

and New Zealand. The Identitarian lambda represents the

Battle of Thermopylae The Battle of Thermopylae ( ; grc, Μάχη τῶν Θερμοπυλῶν, label=Greek, ) was fought in 480 BC between the Achaemenid Persian Empire under Xerxes I and an alliance of Greek city-states led by Sparta under Leonidas I. Lasting o ...

Lower-case letter λ

Examples of the symbolic use of lowercase lambda include: * Lambda indicates the wavelength of any wave, especially in physics, electronic engineering, 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 and radioactivity. This constant is very simply related (by a multiplicative constant) to the half-life of any radioactive material. * In probability theory, lambda represents the density of occurrences within a time interval, as modelled by the Poisson distribution. * In mathematical logic and computer science, lambda is used to introduce

anonymous function In computer programming, an anonymous function (function literal, lambda abstraction, lambda function, lambda expression or block) is a function definition that is not bound to an identifier. Anonymous functions are often arguments being passed to ...

s expressed with the concepts of

lambda calculus Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation ...

. * Lambda indicates an eigenvalue in the mathematics of linear algebra. * In the physics of

electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...

s, lambda sometimes indicates the linear charge density of a uniform line of electric charge (measured in

coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant current in 1 second and to elementary char ...

s 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 The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which d ...

. * In ecology, 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 and in computer science, lambda denotes the empty string. * Lambda is a nonstandard symbol in the

International Phonetic Alphabet The International Phonetic Alphabet (IPA) is an alphabetic system of phonetic transcription, phonetic notation based primarily on the Latin script. It was devised by the International Phonetic Association in the late 19th century as a standa ...

for the voiced alveolar lateral affricate . * Lambda denotes the

Lebesgue measure In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of ''n''-dimensional Euclidean space. For ''n'' = 1, 2, or 3, it coincides wit ...

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 concern ...

. * The Goodman and Kruskal's lambda in

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 An oxygen sensor (or lambda sensor, where lambda refers to air–fuel equivalence ratio, usually denoted by λ) or probe or sond, is an electronic device that measures the proportion of oxygen (O2) in the gas or liquid being analysed. It was ...

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 Failure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. It is usually denoted by the Greek letter λ (lambda) and is often used in reliability engineering. The failure rate of a ...

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 failures. * In criminology, lambda denotes an individual's frequency of offences. * 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 In neurobiology, the length constant (''λ'') is a mathematical constant used to quantify the distance that a graded electric potential will travel along a neurite via passive electrical conduction. The greater the value of the length constant, t ...

(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 The enthalpy of vaporization (symbol ), also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance to transform a quantity of that substance into a gas. T ...

per mole of material (a.k.a. its "latent heat"). * In the technology and science of

celestial navigation Celestial navigation, also known as astronavigation, is the practice of position fixing using stars and other celestial bodies that enables a navigator to accurately determine their actual current physical position in space (or on the surface of ...

, 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'', 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 Alliance s ...

. The lambda symbol became associated with Gay Liberation 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 ''libra'' and Byzantine ''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.

References