TeXipedia

wedge

Represents the wedge product operator in mathematics, commonly used to denote exterior multiplication between differential forms or vectors.

Overview

Essential in advanced mathematics and theoretical physics, particularly in differential geometry, linear algebra, and exterior algebra.

  • Frequently used in multilinear algebra to construct exterior products of vectors and forms
  • Important in physics for describing angular momentum and electromagnetic field tensors
  • Appears regularly in geometric algebra and differential forms
  • Often employed in advanced calculus to express oriented area or volume elements

Examples

Logical AND operator in propositional logic

p∧q  ⟹  rp \wedge q \implies r 
p \wedge q \implies r

Exterior (wedge) product in differential geometry

ω=dx∧dy∧dz\omega = dx \wedge dy \wedge dz 
\omega = dx \wedge dy \wedge dz

Set intersection in lattice theory

a∧b=sup⁡{x:x≤a and x≤b}a \wedge b = \sup\{x : x \leq a \text{ and } x \leq b\} 
a \wedge b = \sup\{x : x \leq a \text{ and } x \leq b\}