✳flâneur — a map of the web's best reading

Hodge star operator - Wikipedia

en.wikipedia.org · 7,867 words · saved by 1 readers

In mathematics, the Hodge star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the operator to an element of the algebra produces the Hodge dual of the element. This map was introduced by W. V. D. Hodge. For example, in an oriented 3-dimensional Euclidean space, an oriented plane can be represented by the exterior product of two basis vectors, and its Hodge dual is the normal vector given by their cross product; conversely, any vector is dual to the oriented plane perpendicular to it, endowed with a suitable bivector. Generalizing this to an n-dimensional vector space, the Hodge star is a one-to-one mapping of k-vectors to (n – k)-vectors; the dimensions of these spaces are the binomial coefficients ( 𝑛 𝑘 ) = ( 𝑛 𝑛 − 𝑘 ) . The naturalness of the star operator means it can play a role in differential geometry when applied to the cotangent bundle of a

Hodge star operator - Wikipedia Jump to content From Wikipedia, the free encyclopedia Exterior algebraic map taking tensors from p forms to n-p forms In mathematics , the Hodge star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form . Applying the operator to an element of the algebra produces the Hodge dual of the element. This map was introduced by W. V. D. Hodge . For example, in an oriented 3-dimensional Euclidean space, an oriented plane can be represented by the exterior

Explore this link on the map →

related reading