TeXipedia

star

Represents a star-shaped operator commonly used in mathematical expressions and decorative elements.

Overview

Serves as both a binary operator in mathematical notation and a decorative symbol in various contexts. Most frequently encountered in:

  • Abstract algebra for special binary operations
  • Ring theory and group theory for specialized product notations
  • Computer science for wildcard operations or special markers
  • Document formatting as a decorative bullet point or separator

The symbol maintains consistent sizing in mathematical mode and can be scaled when used decoratively.

Examples

Binary operation in abstract algebra using star notation.

a⋆b=b⋆aa \star b = b \star a 
a \star b = b \star a

Denoting a special or optimal value in optimization.

x⋆=arg⁡min⁡f(x)x^{\star} = \arg\min f(x) 
x^{\star} = \arg\min f(x)

Representing a dual space in functional analysis.

V⋆={f:V→R}V^{\star} = \{f: V \to \mathbb{R}\} 
V^{\star} = \{f: V \to \mathbb{R}\}