Using the Lambda Symbol
Lambda is the eleventh letter of the Greek alphabet, spelled "lamda" in Unicode's official names because that transliteration was chosen for the standard. The small form looks like an inverted y with a long tail, and it has picked up more distinct technical meanings than almost any other Greek letter.
What λ stands for
- Wavelength in physics: c = fλ, and a 532 nm laser has λ = 532 nm.
- Eigenvalues in linear algebra: Av = λv.
- Rate parameter of a Poisson or exponential distribution, and the decay constant in radioactivity.
- Lambda calculus, Alonzo Church's 1930s formal system, where λx.x + 1 defines a function of x.
- Anonymous functions in programming: Python's lambda x: x + 1, and the "lambda" keyword or arrow functions in Java, C#, Kotlin and JavaScript.
- Lagrange multipliers in constrained optimisation.
Capital Λ is the cosmological constant in the ΛCDM model of the universe, a diagonal matrix of eigenvalues, and the name of a supercooled particle, the lambda baryon.
Typography
λ is a letter, so it behaves like a variable: italic in typeset maths, upright in prose, with a space either side of operators (λ = 2π/k) and none inside a product (2λ). Do not swap in the logical-and wedge ∧, which is a different character with a flat top, or the Latin turned y ʎ from the phonetic alphabet. In code, the ASCII word "lambda" is what the language expects; the Unicode letter is for comments, docs and slides. A handful of languages, including Racket and some Lisp dialects, accept λ as a synonym for the keyword.
Typing it
There is no Latin-1 Alt code and no Option-key combination on the Mac, which makes λ harder to reach than π or Ω. In Word, type 03BB and press Alt + X. On a Mac, add the Greek input source and press L, or search "lambda" in the Character Viewer. iPhone and Android users do the same with a Greek keyboard, where the L key gives λ and Shift + L gives Λ. The HTML entity is λ.
Half-Life and the lambda in culture
Valve's Half-Life series turned the orange λ into one of gaming's most recognised logos, standing for the Lambda Complex at Black Mesa and for the resistance in Half-Life 2. Fans put it in Steam and Discord names, spray-paint it in other games, and pair it with the check mark symbols style "λ ✓" in speedrun bios. Functional programmers wear it on stickers and conference badges, Lambda School and AWS Lambda borrowed the name, and it was adopted in the 1970s as a symbol of gay liberation, which is why it still appears in LGBTQ+ profiles. As a plain Greek letter it renders everywhere text does and sits beside the delta symbol and the sigma symbol in a maths-heavy handle; for the game-logo look, try it in the bold fonts generator.