Lambda — Λ / λ
Lambda (Λ λ) is the eleventh letter of the Greek alphabet. The lambda symbol is written Λ in uppercase and λ in lowercase, and it corresponds to the English "l". In physics λ stands for wavelength and the radioactive decay constant, in linear algebra for an eigenvalue, and in programming for anonymous functions borrowed from lambda calculus; uppercase Λ is the cosmological constant. Copy it with the buttons below, or see how to type Greek letters on any keyboard.
Λ λ
Copy: Λ λ
Unicode code points: U+039B (uppercase), U+03BB (lowercase).
| Uppercase | Λ |
|---|---|
| Lowercase | λ |
| Transliteration | l |
| Pronunciation | LAHM‑thah |
| Numeric value | 30 |
Etymology and Origin
Lambda comes from the Phoenician letter "lamed," meaning "goad" or "ox goad" (a stick for herding cattle). The uppercase lambda (Λ) resembles an inverted V shape. Lambda is the eleventh letter of the Greek alphabet and has diverse applications across mathematics, physics, and computer science.
Pronunciation
- Ancient Greek: [l] as in "lamp"
- Modern Greek: [l] as in "lamp" (unchanged)
- English usage: LAM-duh [ˈlæmdə]
Lambda for Wavelength in Physics
The most ubiquitous use of lambda is to represent wavelength (λ), the distance between successive peaks of a wave. Wavelength is fundamental to understanding all wave phenomena, from light to sound to quantum mechanics.
- Wave equation: c = λf (speed = wavelength × frequency)
- Visible light: λ ranges from ~400 nm (violet) to ~700 nm (red)
- Radio waves: AM radio λ ≈ 300 m, FM radio λ ≈ 3 m
- De Broglie wavelength: λ = h/p for matter waves in quantum mechanics
Uses of Lambda in Mathematics
- Eigenvalues: Av = λv where λ is eigenvalue, v is eigenvector
- Lambda Calculus: λx.x+1 denotes anonymous functions in computer science
- Carmichael Function: λ(n) in number theory
- Lebesgue Measure: λ for measure in analysis
- Poisson Distribution: λ is the rate parameter (mean = variance = λ)
- Empty String: λ represents empty string in formal languages
Uses in Science and Engineering
- Nuclear Physics: Decay constant λ in N(t) = N₀e^(-λt)
- Cosmology: Λ (cosmological constant) in Einstein's field equations
- Thermal Conductivity: λ (alternative to κ) in some notations
- Longitude: λ for geographic longitude (φ is latitude)
- Economics: Lagrange multiplier λ in constrained optimization
- Half-life: t₁/₂ = ln(2)/λ relates half-life to decay constant
Lambda Calculus and Computing
- Lambda Calculus: Formal system invented by Alonzo Church in 1930s
- Anonymous Functions: Python: lambda x: x**2, JavaScript: (x) => x**2
- Functional Programming: Foundation of Lisp, Haskell, Scheme
- AWS Lambda: Serverless computing platform named after λ calculus
- Half-Life: Video game series uses λ symbol as iconic logo
Mathematical Examples with Lambda
Wavelength: Green light at 550 nm: f = c/λ = (3×10⁸)/(550×10⁻⁹) ≈ 5.45×10¹⁴ Hz
Eigenvalue: Matrix [[3,1],[0,2]] has eigenvalues λ₁=3, λ₂=2
Radioactive decay: Carbon-14 has λ = 1.21×10⁻⁴ yr⁻¹, so t₁/₂ ≈ 5730 years
Lambda function: (λx.x²)(5) = 25 in lambda calculus
Poisson distribution: If λ=3 events/hour, P(2 events) = 3²e⁻³/2! ≈ 0.224
Writing Tips
- Uppercase Λ: Inverted V shape - two diagonal strokes meeting at top
- Lowercase λ: Like a stick figure - vertical stroke with diagonal extending up and left
- Common mistake: Lowercase λ is tall like "l" - it rises high but sits on the baseline
- Handwriting: Start at top of lowercase λ, draw down then curve up to the left
Interesting Facts
- Lambda is the ancestor of the Latin letter L
- In ancient Greek numerals, Λ΄ = 30
- Lambda calculus predates computers but became foundation of functional programming
- The cosmological constant Λ was Einstein's "biggest blunder" but is now crucial to dark energy
- Visible light wavelengths are measured in nanometers (10⁻⁹ m)
- Half-Life video game series uses λ logo on protagonist's suit
- Lambda Literary Awards honor LGBTQ+ literature
- AWS Lambda processes trillions of requests per month
- Eigenvalues determine matrix stability, oscillations, and transformations
- Lambda Orionis is a hot blue star forming the head of Orion constellation
Frequently Asked Questions
How do I type λ?
The easiest way is to use the copy buttons at the top of this page. In Microsoft Word, type 03BB and press Alt + X. In HTML, use λ (λ) or Λ (Λ). In LaTeX, use \lambda or \Lambda. With a Greek keyboard layout enabled, press L. See how to type Greek letters for every method.
What does λ mean in physics?
Wavelength, the distance between two wave peaks. For example, green light has λ ≈ 530 nm. λ is also the radioactive decay constant.
What is a lambda function in programming?
A small anonymous function, named after Alonzo Church's lambda calculus. For example, in Python lambda x: x * 2 doubles its input.
Is Λ the same as the logical "and" symbol ∧?
No. Λ (U+039B) is uppercase lambda; ∧ (U+2227) is the logical AND operator. They look similar, but ∧ is usually smaller and sits lower.