Lambda

How to read it

Lambda is said LAM-duh, with no b sound (Cambridge Dictionary: /ˈlæm.də/). Modern Greek spells it λάμδα, “Lamdha” in the University of Arizona’s guide, and Unicode names the letter the same way, LAMDA, with “lambda” as an alias.

Also searched as: lambda letter, lambda symbol, λ, Λ, λ meaning.

Capital, small and look-alike forms

Unicode cross-refers λ to a Latin small letter lambda ꟛ (U+A7DB), a separate character.

Lambda in maths and statistics

In statistics λ is the likelihood ratio of a hypothesis test; Jeff Miller’s history of mathematical symbols says Jerzy Neyman and Egon Pearson introduced it in 1928. In logic and computer science the λ-calculus is, in the Stanford Encyclopedia of Philosophy’s words, “a simple notation for functions and application”. In Python, lambda expressions create anonymous functions (Python Language Reference).

In AI and machine learning

λ is the regularisation rate, the number that sets the relative importance of regularisation during training. Google’s Machine Learning Glossary says it is usually represented by lambda, and that raising it reduces overfitting but may reduce the model’s predictive power. PyTorch’s optimisers use λ for weight decay, adding λθ to each gradient. scikit-learn calls the same setting Alpha: the constant that multiplies the L2 penalty in ridge regression.

In quantum physics

λ is the de Broglie wavelength. OpenStax’s University Physics says any particle that has energy and momentum is a de Broglie wave, with wavelength λ = h/p, Planck’s constant divided by the particle’s momentum.

Other uses of lambda

In chemistry and physics λ is the wavelength of any wave, including electromagnetic radiation: OpenStax’s Chemistry 2e gives λ for wavelength beside ν (nu) for frequency. In radioactive decay λ is the decay constant, in the law −dN/dt = λN (OpenStax, University Physics).