TeXipedia

odot

Represents a binary operation denoted by a dot within a circle, commonly used in mathematical notation for specialized product operations.

Overview

Appears frequently in advanced mathematics and physics to denote specific types of product operations or group actions.

  • Common in abstract algebra for describing circular product operations
  • Used in tensor calculus and differential geometry
  • Often represents specialized dot products or composition operations in mathematical physics
  • Particularly useful in group theory and ring theory where circular operations need to be distinguished from standard multiplication or dot products

Examples

Defining a binary operation on a vector space.

V⊙W={v⊙w:v∈V,w∈W}V \odot W = \{v \odot w : v \in V, w \in W\} 
V \odot W = \{v \odot w : v \in V, w \in W\}

Expressing the Hadamard (element-wise) product of matrices.

A⊙B=(a11b11a12b12a21b21a22b22)A \odot B = \begin{pmatrix} a_{11}b_{11} & a_{12}b_{12} \\ a_{21}b_{21} & a_{22}b_{22} \end{pmatrix} 
A \odot B = \begin{pmatrix} a_{11}b_{11} & a_{12}b_{12} \\ a_{21}b_{21} & a_{22}b_{22} \end{pmatrix}

Representing the solar symbol in astronomical equations.

L⊙=3.828×1026 WL_{\odot} = 3.828 \times 10^{26} \text{ W} 
L_{\odot} = 3.828 \times 10^{26} \text{ W}