TeXipedia

bigwedge

Represents a large wedge operator used for denoting multiple logical conjunctions or exterior products in mathematics.

Overview

Serves as an n-ary operator primarily found in advanced mathematics and logic, particularly useful in linear algebra, differential geometry, and formal logic.

  • Common in exterior algebra for expressing wedge products of multiple differential forms
  • Used to denote the conjunction of multiple logical statements in mathematical logic
  • Appears frequently in multilinear algebra when describing antisymmetric tensor products
  • Often employed in theoretical physics and advanced geometry for expressing mathematical relationships between multiple vectors or forms

Examples

Logical conjunction over multiple propositions.

⋀i=1nPi\bigwedge_{i=1}^n P_i 
\bigwedge_{i=1}^n P_i

Exterior product of multiple differential forms.

ω=⋀i=13dxi\omega = \bigwedge_{i=1}^3 dx_i 
\omega = \bigwedge_{i=1}^3 dx_i

Intersection of multiple sets.

⋀k=1mAk=A1∧A2∧⋯∧Am\bigwedge_{k=1}^m A_k = A_1 \wedge A_2 \wedge \cdots \wedge A_m 
\bigwedge_{k=1}^m A_k = A_1 \wedge A_2 \wedge \cdots \wedge A_m