TeXipedia

boxplus

Represents a binary operator combining addition with a box shape, commonly used in mathematical notation and abstract algebra.

Overview

Serves as a specialized mathematical operator that combines visual elements of both a box and a plus sign, making it particularly useful in contexts where a distinct addition-like operation needs to be distinguished from standard addition.

  • Frequently appears in abstract algebra and group theory to denote special binary operations
  • Used in mathematical logic and set theory for specialized operations
  • Common in academic papers and advanced mathematical texts where custom operators help distinguish between different types of addition-like operations
  • Particularly useful when multiple addition-like operations need to be visually distinct within the same context

Examples

Boolean algebra expression showing the exclusive OR operation.

A⊞B=(A∧¬B)∨(¬A∧B)A \boxplus B = (A \land \neg B) \lor (\neg A \land B) 
A \boxplus B = (A \land \neg B) \lor (\neg A \land B)

Direct sum of vector spaces in linear algebra.

V=U1⊞U2⊞U3V = U_1 \boxplus U_2 \boxplus U_3 
V = U_1 \boxplus U_2 \boxplus U_3

Orthogonal sum operation in quantum mechanics.

H=H1⊞H2\mathcal{H} = \mathcal{H}_1 \boxplus \mathcal{H}_2 
\mathcal{H} = \mathcal{H}_1 \boxplus \mathcal{H}_2