In mathematics, the exterior product or wedge product of vectors is an algebraic construction generalizing certain features of the cross product to higher dimensions. Like the cross product, and the scalar triple product, the exterior product of vectors is used in Euclidean geometry to study areas, volumes, and their higher-dimensional analogs. Also like the cross product, the exterior product is alternating, meaning that for all vectors u, or eq...
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In mathematics, the exterior product or wedge product of vectors is an algebraic construction generalizing certain features of the cross product to higher dimensions. Like the cross product, and the scalar triple product, the exterior product of vectors is used in Euclidean geometry to study areas, volumes, and their higher-dimensional analogs. Also like the cross product, the exterior product is alternating, meaning that for all vectors u, or equivalently for all vectors u and v. In linear algebra, the exterior product provides an abstract algebraic manner for describing the determinant and the minors of a linear transformation that is basis-independent, and is fundamentally related to ideas of rank and linear independence.
The exterior algebra (also known as the Grassmann algebra, after Hermann Grassmann) of a given vector space V over a field K is the unital associative algebra Λ(V) generated by the exterior product. It is widely used in contemporary geometry, especially...
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