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

Peter Lewintan

doi:10.1515/math-2021-0115

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arXiv · 2105.13130

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

Peter Lewintan

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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 $n\ge2$.

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Peter Lewintan. 2021-05-26. Matrix representation of a cross product and related curl-based differential operators in all space dimensions. https://doi.org/10.1515/math-2021-0115

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