crossoperator

Crossoperator is a term used in mathematics and computer science to denote a cross-related binary operator. It is not a single standardized concept, but a label that appears in some texts for operations that combine two operands in a way that encodes a perpendicular or rotational relationship between them.

In mathematics, the most common instance associated with the name is the cross product operator, typically written as ×. The cross operator maps two vectors in three-dimensional space to a third vector that is perpendicular to both inputs. It is bilinear and anti-symmetric, satisfying a × a = 0 and a × b = −(b × a). The magnitude of a × b equals the area of the parallelogram spanned by a and b, and its direction is given by the right-hand rule. In Euclidean 3-space, the cross product is closely related to the exterior product via the Hodge dual, and it plays a central role in physics and engineering, for example in torque and angular momentum calculations.

Generalizations of crossoperator exist in higher-dimensional or more abstract algebraic settings, where cross-like operations preserve some combination of bilinearity, anti-symmetry, and perpendicularity, but a direct analogue of the three-dimensional cross product is not unique outside 3D space.

In computing and programming, a crossoperator may refer to the function or operator that implements such a cross-like combination of two vectors, commonly provided as a cross product routine in numerical and graphics libraries.

See also: cross product, vector product, exterior algebra, wedge product.