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intercal

Represents a binary operation denoting an abstract product or intercalation between mathematical objects.

Overview

Primarily used in advanced mathematics and theoretical computer science to denote specialized binary operations or transformations between structures.

  • Common in category theory and abstract algebra for describing certain types of products or compositions
  • Appears in formal specifications and theoretical computer science literature
  • Often employed when standard multiplication or composition symbols are already used for other operations
  • Useful in contexts where a distinct binary operation symbol is needed to avoid ambiguity

Examples

Expressing the transpose of a matrix multiplication.

A⊺B=(BA)⊺A \intercal B = (BA)\intercal 
A \intercal B = (BA)\intercal

Denoting the orthogonal complement of a subspace V.

V⊺={w:⟨v,w⟩=0 for all v∈V}V^{\intercal} = \{w : \langle v,w \rangle = 0 \text{ for all } v \in V\} 
V^{\intercal} = \{w : \langle v,w \rangle = 0 \text{ for all } v \in V\}

Representing the adjoint operator in functional analysis.

T⊺:Y∗→X∗T^{\intercal}: Y^* \to X^* 
T^{\intercal}: Y^* \to X^*