TeXipedia

bigodot

Represents a large circle operator commonly used for denoting mathematical operations or relations over indexed sets.

Overview

Serves as a binary operator in advanced mathematical notation, particularly useful in abstract algebra and theoretical mathematics.

  • Often employed to denote specialized product operations or compositions over indexed families of elements
  • Frequently appears in group theory and algebraic structures to represent circular operations
  • Useful in expressing complex mathematical relationships where standard multiplication or addition notation is insufficient
  • Common in advanced textbooks and research papers where specialized notation is needed for abstract concepts

Examples

Direct product of vector spaces in linear algebra.

V=V1⨀V2⨀V3V = V_1 \bigodot V_2 \bigodot V_3 
V = V_1 \bigodot V_2 \bigodot V_3

Representing a cyclic group operation in abstract algebra.

G=⨀i=1nGiG = \bigodot_{i=1}^n G_i 
G = \bigodot_{i=1}^n G_i

Notation for a specialized tensor product in quantum mechanics.

∣ψ⟩=⨀j=1N∣ϕj⟩\ket{\psi} = \bigodot_{j=1}^N \ket{\phi_j} 
\ket{\psi} = \bigodot_{j=1}^N \ket{\phi_j}