Lambdawert

LambdaWert is a German term used to denote the quantity λ in various disciplines. It does not designate a single constant; its meaning depends on context. In mathematics and statistics, λ commonly denotes a rate or an eigenvalue. In a Poisson process, λ is the average rate of events per unit time, governing the probability of counts: P(N(t)=k) = e^{-λ t} (λ t)^k / k!. In linear algebra, λ denotes eigenvalues that satisfy det(A - λI) = 0. In survival analysis or reliability, the hazard or failure rate is often written λ(t). In optimization, λ is the Lagrange multiplier associated with a constraint in the Lagrangian L = f(x) + λ g(x). In regression and machine learning, λ is a regularization parameter that controls the strength of penalties such as ridge (L2) or lasso (L1). In physics, λ may denote wavelength, with the relation λ = c / f for light in a vacuum, where c is the speed of light and f the frequency. The symbol is widely reused to denote different kinds of rate, scale, or spectral quantity, so the precise interpretation should be specified in the surrounding text.