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Lambda

Represents a capital lambda letter from the Greek alphabet, commonly used in mathematics and physics for various mathematical concepts and constants.

Overview

A versatile symbol widely used across multiple scientific and mathematical domains:

  • Frequently appears in linear algebra to denote eigenvalues
  • Used in physics to represent wavelength and decay constants
  • Common in computer science for lambda calculus and functional programming concepts
  • Appears in statistics and probability theory for rate parameters in Poisson distributions
  • Essential in quantum mechanics and particle physics notation

Examples

Defining a Poisson process rate parameter.

P(X=k)=Λke−Λk!P(X = k) = \frac{\Lambda^k e^{-\Lambda}}{k!} 
P(X = k) = \frac{\Lambda^k e^{-\Lambda}}{k!}

Representing the eigenvalue matrix in linear algebra.

A=PΛP−1A = P\Lambda P^{-1} 
A = P\Lambda P^{-1}

Denoting the decay constant in radioactive decay.

N(t)=N0e−ΛtN(t) = N_0 e^{-\Lambda t} 
N(t) = N_0 e^{-\Lambda t}