Published Paper

Inserted: 26 may 2021
Last Updated: 19 jan 2022

Journal: Open Mathematics
Volume: 19
Number: 1
Pages: 1330-1348
Year: 2021
Doi: 10.1515/math-2021-0115

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 .

Keywords: div-curl lemma, generalized curl, Generalized cross product, Jacobi’s identity, vector Laplacian, Helmholtz decomposition, matrix representation

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