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.

[hongy...@gmail.com]

See the following description given on <https://en.wikipedia.org/wiki/Hodge_star_operator>:

<quote>
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.
</quote>

The noun phrase used in the first sentence, i.e., the following one is very long:

a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form.

Any hints of the rewriting/touch up/comments on it will be highly appreciated.

Regards,
HY

[semir...@my-deja.com]

Although long it seems to be clearly set out.

As long as the reader knows the meaning of the various terms, I would say that it is fine.