Hodge Dual

In mathematics, the Hodge star operator or Hodge dual is a significant linear map introduced in general by W. V. D. Hodge. It is defined on the exterior algebra of a finite-dimensional oriented inner product space.

Read more about Hodge Dual:  Dimensionalities and Algebra, Extensions, Formal Definition of The Hodge Star of k-vectors, Explanation, Computation of The Hodge Star, Index Notation For The Star Operator, Examples, Inner Product of k-vectors, Duality, Hodge Star On Manifolds, Derivatives in Three Dimensions

Other articles related to "hodge dual, hodge":

Hodge Dual - Derivatives in Three Dimensions
... on 1-forms that in components is the operator Applying the Hodge star gives The final case prefaced and followed by, takes a 1-form to a 0-form (function) written out in components it is ... in terms of the exterior derivative and the Hodge star ...
Bivector - Three Dimensions - Axial Vectors
... More precisely, the Hodge dual gives the isomorphism between axial vectors and bivectors, so each axial vector is associated with a bivector and vice-versa that is where ... as when written as determinants they are calculated in the same way so are related by the Hodge dual Bivectors have a number of advantages over axial vectors ...

Famous quotes containing the word dual:

    Thee for my recitative,
    Thee in the driving storm even as now, the snow, the winter-day
    declining,
    Thee in thy panoply, thy measur’d dual throbbing and thy beat
    convulsive,
    Thy black cylindric body, golden brass and silvery steel,
    Walt Whitman (1819–1892)