Symbols:Greek/Lambda
Contents
Lambda
The $11$th letter of the Greek alphabet.
- Minuscule: $\lambda$
- Majuscule: $\Lambda$
The $\LaTeX$ code for \(\lambda\) is \lambda .
The $\LaTeX$ code for \(\Lambda\) is \Lambda .
Von Mangoldt Function
- $\Lambda \left({n}\right)$
The von Mangoldt function $\Lambda: \N \to \R$ is defined as:
- $\Lambda \left({n}\right) = \begin{cases} \ln \left({p}\right) & : \exists m \in \N, p \in \mathbb P: n = p^m \\ 0 & : \text{otherwise} \end{cases}$
where $\mathbb P$ is the set of all prime numbers.
The $\LaTeX$ code for \(\Lambda \left({n}\right)\) is \Lambda \left({n}\right) .
Linear Density
- $\lambda$
Used to denote the linear density of a given one-dimensional body:
- $\displaystyle \lambda = \frac m l$
where:
Parameter of Poisson Distribution
- $\lambda$
Used to denote the parameter of a given Poisson distribution:
Let $X$ be a discrete random variable on a probability space $\left({\Omega, \Sigma, \Pr}\right)$.
Then $X$ has the Poisson distribution with parameter $\lambda$ (where $\lambda > 0$) if:
- $\operatorname{Im} \left({X}\right) = \left\{{0, 1, 2, \ldots}\right\} = \N$
- $\displaystyle \Pr \left({X = k}\right) = \frac 1 {k!} \lambda^k e^{-\lambda}$
Left Regular Representation
- $\lambda_a$
Let $\left ({S, \circ}\right)$ be an algebraic structure.
The mapping $\lambda_a: S \to S$ is defined as:
- $\forall a \in S: \map {\lambda_a} x = a \circ x$
This is known as the left regular representation of $\struct {S, \circ}$ with respect to $a$.
The $\LaTeX$ code for \(\lambda_a\) is \lambda_a .
