TeXipedia

Sigma

Represents summation in mathematical expressions, indicating the addition of a sequence of terms.

Overview

Essential in mathematical notation across diverse fields, particularly in series calculations, statistics, and linear algebra.

  • Commonly used to express finite and infinite sums
  • Fundamental in expressing variance and covariance in statistics
  • Key notation in matrix algebra for representing sum of elements
  • Appears frequently in computational algorithms and discrete mathematics
  • Often paired with subscripts and superscripts to define summation bounds

Examples

Defining a covariance matrix in statistics using uppercase sigma.

Σ=(σ12σ12σ21σ22)\Sigma = \begin{pmatrix} \sigma_1^2 & \sigma_{12} \\ \sigma_{21} & \sigma_2^2 \end{pmatrix} 
\Sigma = \begin{pmatrix} \sigma_1^2 & \sigma_{12} \\ \sigma_{21} & \sigma_2^2 \end{pmatrix}

Representing the sum of all elements in a matrix.

tr(Σ)=σ12+σ22\text{tr}(\Sigma) = \sigma_1^2 + \sigma_2^2 
\text{tr}(\Sigma) = \sigma_1^2 + \sigma_2^2

Denoting a sigma-algebra in probability theory.

P(A∣Σ)=P(A∩Σ)P(Σ)P(A \mid \Sigma) = \frac{P(A \cap \Sigma)}{P(\Sigma)} 
P(A \mid \Sigma) = \frac{P(A \cap \Sigma)}{P(\Sigma)}