antivectoriel

Antivectoriel is a term used in French-language mathematics and physics to describe objects that are in some sense opposite to or dual of vectors. It is not a fixed or universally standardized notion; its precise meaning depends on the context and author. In general, antivectorial objects are those that transform contragrediently to ordinary vectors under a linear change of coordinates, or that play the role of duals in a given pairing.

In linear algebra, the most common antivectorial counterpart is the covector (one-form), an element of the dual space V* that linearly maps vectors to scalars. Covectors transform with the inverse transpose when the underlying basis changes, which is the dual behavior to how vectors transform. The exterior algebra extends the idea to antisymmetric multilinear objects; k-forms are often described as antisymmetric antivectorial structures relative to V. In older or intuitive language, these dual or antisymmetric objects are sometimes loosely referred to as antivectors.

In geometry and physics, related concepts include pseudovectors (axial vectors), which transform with the determinant of a transformation, and more generally antisymmetric tensors that encode oriented or dual information.

Because antivectoriel is not a standard technical term, precise usage is found in field-specific texts. When encountered, it usually signals a discussion of duality, antisymmetry, or orientation-related properties in relation to vectors.

See also: vector, covector, dual space, exterior algebra, differential form, pseudovector, orientation.