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 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

Examples of the symbolic use of lowercase lambda include: * Lambda indicates the wavelength of any wave, especially in physics, electronic engineering, and 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 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, lambda represents the density of occurrences within a time interval, as modelled by the Poisson distribution. * In mathematical logic and

, lambda is used to introduce anonymous functions expressed with the concepts of lambda calculus. * Lambda indicates an eigenvalue in the mathematics of linear algebra. * 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 multivariable calculus, multi-dimensional calculus. * In solid-state electronics, lambda indicates the channel length modulation parameter of a MOSFET. * 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 matrix (mathematics), matrix. * In formal language theory and in computer science, lambda denotes the empty string. * 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 . * Lambda denotes the Lebesgue measure in Set theory, mathematical set theory. * 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. * 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. * A Lambda (rocket), Lambda 4S solid-fuel rocket was used to launch Ohsumi (satellite), Japan's first orbital satellite in 1970. * 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. * In criminology, lambda denotes an individual's frequency of Offence (law), offences. * In

, 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 (unit), mole of material (a.k.a. its "latent heat"). * 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'', 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 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 lambda symbol became associated with Gay Liberation and recognized as an LGBT symbols, LGBT symbol for some time afterwards, being used as such by the International Gay Rights Congress in Edinburgh.

Litra symbol

The Roman units, Roman ''libra'' and Byzantine units, 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), 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