Lambda

Lambda (uppercase Λ, lowercase λ; Greek: Λάμ(β)δα lam(b)da) is the 11th letter of the Greek alphabet. In the system of Greek numerals lambda has a value of 30. Lambda is related to the Phoenician letter Lamed . Letters in other alphabets that stemmed from lambda include the Latin L and the Cyrillic letter El (Л, л). The ancient grammarians and dramatists give evidence to the pronunciation as [laːbdaː] (λάβδα) in Classical Greek times.^[1] In Modern Greek the name of the letter, Λάμδα, is pronounced [lamða]; the spoken letter itself has the sound of "l" as with Latinate "L".

In early Greek alphabets, the shape and orientation of lambda varied.^[2] 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.^[3] The Unicode numbers for lambda are U+039B and U+03BB.

The Greek alphabet on a black figure vessel, with a Phoenician-lamed-shaped lambda. (The gamma has the shape of modern lambda.)

Symbol

Upper-case letter Λ

• 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.
• Lambda was used as a shield pattern by the Spartan Army. This stood for Lacedaemon, (Λακεδαίμων, Lakedaímōn), the name of the region of Sparta.^[4]
• Lambda is the von Mangoldt function in mathematical number theory.
• 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 (mathematics).
• 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 neighborhood, satisfying the current definition of a planet.
• In crystal optics, lambda is used to represent the period of a lattice.
• In NATO military operations, a chevron (a capital lambda symbol) is painted on the vehicles of this military alliance for identification.
• In chemistry there are Δ (delta) and Λ (lambda) isomers, see: coordination complex
• In electrochemistry, lambda denotes the "equivalent conductance" of an electrolyte solution.
• In cosmology, lambda is the symbol for the cosmological constant.
• In optics, lambda denotes the grating pitch of a Bragg reflector.
• In handwritten Russian, this letter represents Л in both uppercase and lowercase formats.

Lower-case letter λ

Lower-case lambda

• 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 wavelength of any wave, especially in physics, electronics engineering, and mathematics.^[5]
• 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 modeled by the Poisson distribution.
• In mathematical logic and computer science, lambda is used to introduce anonymous functions expressed with the concepts of lambda calculus.
• Lambda is a unit of volume, synonymous with one microliter (1 μL), that is, one cubic millimetre (1 mm³). This use is currently deprecated.
• 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 multi-dimensional calculus.
• In solid-state electronics, lambda indicates the channel length modulation parameter of a MOSFET.
• There is a lambda phage virus in biology.
• 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).
• In formal language theory and in computer science, lambda denotes the empty string.
• Lambda is a nonstandard symbol in the International Phonetic Alphabet.
• In telecommunications, lambda indicates the wavelength in a wavelength-division multiplexing optical communications system. This is actually a form of the long-established concept of frequency-division multiplexing.
• Lambda denotes the Lebesgue measure in 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-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.^[6]
• 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 offenses.
• In cartography and navigation, lambda denotes the longitude of a location.
• Lambda is the symbol of the musician Richard D. James or Aphex Twin.
• Lambda denotes Christopher Langton's parameter for the classification of Stephen Wolfram's classes of cellular automata.
• 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").^[7]
• In the technology and science of celestial navigation, lambda denotes the longitude as opposed to the Roman letter "L", which denotes the latitude.
• King Louis XIII of France used the letter lambda as his personal symbol rather than monogram.
• In Volvo automobiles, lambda denotes an engine, fuel, or ignition system failure.
• 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 lambda was selected as a symbol by the Gay Activists Alliance of New York in 1970, and declared the international symbol for gay and lesbian rights by the International Gay Rights Congress in Edinburgh, Scotland, in 1974.
• The "lambda sign" is used for diagnosis of dichorionic twins in obstetric ultrasonography
• In bifurcation theory, lambda is used to parameterize a family of differential equations
• Lambda was used by Pythagoras to denote the "Lambda number sequence" 1, 2, 3, 4, 9, 8, 27, ...,(sequence A098293 in OEIS) formed by the integers of the form 2ⁱ and 3ⁱ, for nonnegative integer i.

Litra symbol

The Roman libra and Byzantine lítra (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 (as λͅ). These are variously encoded in Unicode. The Ancient Greek Numbers Unicode block includes 10183 GREEK LITRA SIGN (𐆃) as well as 𐅢, which is described as 10162 GREEK ACROPHONIC HERMIONIAN TEN^[8] but was much more common as a form of the litra sign. A variant of the sign can be formed from 0338 COMBINING LONG SOLIDUS OVERLAY and either 039B GREEK CAPITAL LETTER LAMDA (Λ̸) or 03BB GREEK SMALL LETTER LAMDA (λ̸).^[9]

Lambda as a programming construct

• In programming languages such as Lisp, Python and Ruby lambda is an operator used to denote anonymous functions or closures, following the usage of lambda calculus. An example of this use of lambda in the Python language is this section of computer code that sorts a list alphabetically by the last character of each entry:

  >>> list = ['woman', 'man', 'horse', 'boat', 'plane', 'dog']
  >>> sorted(list, key = lambda word: (word[-1]))
  ['horse', 'plane', 'dog', 'woman', 'man', 'boat']
  

• In the C# programming language a lambda expression is an anonymous function that can contain expressions and statements.^[10]
• The language Unlambda is a functional programming language based upon combinatory logic, a simplification of the lambda calculus that does not involve the lambda at all, hence the un- prefix.

Lambda as a name

• Stargate SG-1 uses a modified upper-case lambda, with a small circle above the apex, to indicate Earth. This symbol has since become associated with the entire franchise.^[11][12]
• Brothers of the Lambda Theta Phi Latin Fraternity are considered Lambda Men, or simply Lambdas.
• The popular science fiction universe of Star Wars uses a transport vehicle known as the Lambda-class shuttle that when viewed forward has the shape of the lowercase lambda.^[13]
• Lambda is occasionally used in graphic design to represent a stylised 'A'. Examples include the Disney movie Atlantis: The Lost Empire, the logo of the band Angels & Airwaves, the logo of the band Dream Theater, the logo of electronics company Samsung, and the logo of the engineering consultancy Atkins. Conversely, the name of the band Λucifer (pronounced lucifer) is sometimes spelled Aucifer.
• The upper-case lambda is used as the alias of Providence, Rhode Island based musician Xavier Valentine.^[14]
• The Half-Life franchise of video games uses an encircled block style lower-case lambda as the franchise logo (Half-Life 2 adds the numeral 2 into the logo as superscript), prominently featured on the chest of Gordon Freeman's (the protagonist) powered armor, known as an HEV suit. In the first game, the logo appears at the entrances of the Black Mesa Research Facility's Lambda Complex, which conducted teleportation research. In Half-Life 2 and its Episodes, the encircled block lambda is the universal symbol of the Resistance, often spraypainted to mark the location of safehouses and hidden supply caches; full-time Resistance members wear armbands containing a lower-case lambda without the circle.
• In the 2D fighting game series BlazBlue, a recurring character named Lambda-11 appears in the various games' story modes and as a playable character.
• Several LGBT rights organizations, such as Lambda Legal and the Lambda Literary Award derive their names from the use of a lower-case lambda as a symbol for LGBT rights.
• In the Visual Novel Umineko: When They Cry, there is a character named Lambdadelta.
• In the RPG game Tales of Graces, originally made for the Wii, Lambda is the name of the main story's antagonist (voiced by Keith Silverstein). Lambda was originally a spirit inhabiting the body of a young boy being cared for by Doctor Cornell. However, Emeraulde sees Lambda as a tool, proving it by injecting his cells into monsters and has the ability to control them telepathically. She attempts to destroy Lambda, but he escapes to the artificial planetary satellite Ephinea, with Cornell sacrificing his life to make sure he lives. Arriving on the satellite, Lambda was shunned by humanity and was hunted by Emeraulde, who sends Sophie, a humanoid creation designed to destroy Lambda, down to eliminate it. Over the centuries following, Lambda grew to hate and despise humanity. At the start of the game, Lambda attacks Asbel, Hubert, Cheria, and Richard when they were kids. After yet another defeat by Sophie, Lambda finds a kindred spirit in Richard, who's suffering just as he did and the two fuse. 7 years later, Lambda sets about in Richards body to absorb all the Eleth from all the Valkynies Cryas in the world so he can grow in power and fuse with the Lastalia, the planet's core so he can exterminate humanity so that he can stop the pain caused both to him and to the planet by humanity's wars and fears. Upon defeat, Asbel voluntarily decides to be Lambda's host, with the hero's left eye serving as it's resting place as it goes into a deep sleep, so he can see that humanity can change. in the Lineage and Legacies epilogue, which takes place 6 months after the core game, Asbel had gotten used to Lambda living in his eye, though whenever he has doubts or strong fears, his eye hurts, likely as a result of Lambda reacting to the negative emotions. During a battle against Wyverns, Lambda awakens and allows Asbel to use his power. During the final battle against Fodra, the living sentient core of the planet who also despises humanity because of the desolation caused to her world, Asbel fuses with Lambda for a short moment and absorbs Fodra so that Lambda, as Asbel did for him, can show that humanity can change. He and Fodra go to a deep slumber after the battle.
• There is a PlayStation Vita game known as Cytus Lambda.
• The musical group Axwell Λ Ingrosso use the lambda as symbol in their name.
• An automotive oxygen sensor (O₂ sensor) is also known as a lambda probe, sensor, sond, or sonde.
• Lambda is used in art and photography to refer to a digital Type C print, or to the equipment that is used to produce it.
• In the study of gasoline engines, Lambda sometimes refers to the air/fuel mixture going into the engine.
• In the popular Japan based; light novel, animated series, and manga; "Full Metal Panic!","Full Metal Panic? Fumoffu", and "Full Metal Panic! The Second Raid", it utilizes a machine called a "Lambda Driver". The "Lambda Driver" is a piece of dark technology that is added on an "Arm Slave". The Lambda Driver is a powerful machine that is used by specified characters, which allows the character's Arm Slave to manipulate matter by just concentrating about it.

Character encodings

Unicode uses the spelling "lamda" in character names, instead of "lambda".

• Greek Lambda / Coptic Laula

Character	Λ		λ		ᴧ		Ⲗ		ⲗ
Unicode name	GREEK CAPITAL LETTER LAMDA		GREEK SMALL LETTER LAMDA		GREEK LETTER SMALL CAPITAL LAMDA		COPTIC CAPITAL LETTER LAULA		COPTIC SMALL LETTER LAULA
Encodings	decimal	hex	decimal	hex	decimal	hex	decimal	hex	decimal	hex
Unicode	923	U+039B	955	U+03BB	7463	U+1D27	11414	U+2C96	11415	U+2C97
UTF-8	206 155	CE 9B	206 187	CE BB	225 180 167	E1 B4 A7	226 178 150	E2 B2 96	226 178 151	E2 B2 97
Numeric character reference	Λ	Λ	λ	λ	ᴧ	ᴧ	Ⲗ	Ⲗ	ⲗ	ⲗ
Named character reference	Λ		λ
DOS Greek	138	8A	162	A2
DOS Greek-2	182	B6	229	E5
Windows 1253	203	CB	235	EB
TeX	\Lambda		\lambda

• Mathematical Lambda

Character	𝚲		𝛌		𝛬		𝜆		𝜦		𝝀
Unicode name	MATHEMATICAL BOLD CAPITAL LAMDA		MATHEMATICAL BOLD SMALL LAMDA		MATHEMATICAL ITALIC CAPITAL LAMDA		MATHEMATICAL ITALIC SMALL LAMDA		MATHEMATICAL BOLD ITALIC CAPITAL LAMDA		MATHEMATICAL BOLD ITALIC SMALL LAMDA
Encodings	decimal	hex	decimal	hex	decimal	hex	decimal	hex	decimal	hex	decimal	hex
Unicode	120498	U+1D6B2	120524	U+1D6CC	120556	U+1D6EC	120582	U+1D706	120614	U+1D726	120640	U+1D740
UTF-8	240 157 154 178	F0 9D 9A B2	240 157 155 140	F0 9D 9B 8C	240 157 155 172	F0 9D 9B AC	240 157 156 134	F0 9D 9C 86	240 157 156 166	F0 9D 9C A6	240 157 157 128	F0 9D 9D 80
UTF-16	55349 57010	D835 DEB2	55349 57036	D835 DECC	55349 57068	D835 DEEC	55349 57094	D835 DF06	55349 57126	D835 DF26	55349 57152	D835 DF40
Numeric character reference	𝚲	𝚲	𝛌	𝛌	𝛬	𝛬	𝜆	𝜆	𝜦	𝜦	𝝀	𝝀

Character	𝝠		𝝺		𝞚		𝞴
Unicode name	MATHEMATICAL SANS-SERIF BOLD CAPITAL LAMDA		MATHEMATICAL SANS-SERIF BOLD SMALL LAMDA		MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL LAMDA		MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL LAMDA
Encodings	decimal	hex	decimal	hex	decimal	hex	decimal	hex
Unicode	120672	U+1D760	120698	U+1D77A	120730	U+1D79A	120756	U+1D7B4
UTF-8	240 157 157 160	F0 9D 9D A0	240 157 157 186	F0 9D 9D BA	240 157 158 154	F0 9D 9E 9A	240 157 158 180	F0 9D 9E B4
UTF-16	55349 57184	D835 DF60	55349 57210	D835 DF7A	55349 57242	D835 DF9A	55349 57268	D835 DFB4
Numeric character reference	𝝠	𝝠	𝝺	𝝺	𝞚	𝞚	𝞴	𝞴

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

• Greek letters used in mathematics, science, and engineering
• Л, л - El (Cyrillic)
• Fraser alphabet#Consonants
• Half-Life (video game)

References

1. Herbert Weir Smyth. A Greek Grammar for Colleges. I.1.c
2. "Epigraphic Sources for Early Greek Writing". Poinikastas.csad.ox.ac.uk. Retrieved 2011-10-03.
3. World Wide Web Consortium W3C. HTML 4.01 Spec3ification, 24. Character entity references in HTML 4.
4. This piece of information comes from Photius' Lexicon (see Duncan Campbell, Spartan Warrior 735-331 BC, Osprey Publishing, 2012, p. 28.).
5. Nelkon, Michael (1977). Fundamentals of Physics. St. Albans, Hertfordshire: Hart-Davis Educational. p. 329.
6. "Encyclopedia Astronautica: Lambda". www.astronautix.com. Retrieved 2012-12-18.
7. Wankat Separation Process Engineering 2nd ed, Prentice Hall
8. Unicode Ancient Greek Numbers block.
9. Thesaurus Linguae Graecae.
10. "Lambda Expressions (C# Programming Guide)". Msdn.microsoft.com. Retrieved 2011-10-03.
11. Read, David (July 15, 2010). "Earth Symbol". Propworx. Retrieved 2010-10-12.
12. "Official Stargate Website". Metro-Goldwyn-Mayer. Retrieved 2010-10-13.
13. "Imperial Lambda-class shuttle". Star Wars Databank. Lucasfilm. Retrieved 2010-10-12.
14. "Ʌ". Aarrcc.bandcamp.com. Retrieved 2011-10-03.