Matrix representation of a cross product and related curl-based differential operators in all space dimensions - Archive ouverte HAL Access content directly
Journal Articles Open Mathematics Year : 2021

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

Abstract

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 ≥ 2 .
Fichier principal
Vignette du fichier
Lew_crossN.preprint.pdf (278.08 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03233545 , version 1 (24-05-2021)
hal-03233545 , version 2 (21-01-2022)

Licence

Identifiers

Cite

Peter Lewintan. Matrix representation of a cross product and related curl-based differential operators in all space dimensions. Open Mathematics, 2021, 19 (1), pp.1330-1348. ⟨10.1515/math-2021-0115⟩. ⟨hal-03233545v2⟩

Collections

TDS-MACS
110 View
527 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More