Matrix representation of a cross product and related curl-based differential operators in all space dimensions

Autor:	Lewintan Peter
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	generalized cross product jacobi identity generalized curl matrix representation vector laplacian helmholtz decomposition div-curl lemma 15a24 15a69 47a06 35j05 Mathematics QA1-939
Zdroj:	Open Mathematics, Vol 19, Iss 1, Pp 1330-1348 (2021)
Druh dokumentu:	article
ISSN:	2391-5455
DOI:	10.1515/math-2021-0115
Popis:	A higher dimensional generalization of the cross product is associated with an adequate matrix multiplication. This index-free view allows for a better understanding of the underlying algebraic structures, among which are generalizations of Grassmann’s, Jacobi’s and Room’s identities. Moreover, such a view provides a higher dimensional analogue of the decomposition of the vector Laplacian, which itself gives an explicit index-free Helmholtz decomposition in arbitrary dimensions n≥2n\ge 2.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/5d49f894c0e146efa857e86d3d490e1a Zobrazit plný text záznamu View record in DOAJ