Some Remarks on a Generalized Vector Product

TL;DR

This paper explores a generalized vector product to construct an exterior form on b^{n} and investigates its properties, including a reversing operation for special vector classes, expanding the mathematical understanding of vector algebra.

Contribution

It introduces a generalized vector product and an exterior form for b^{n}, and studies a reversing operation for palindromic and antipalindromic vectors, extending existing vector algebra concepts.

Findings

Defined a new exterior form using a generalized vector product

Introduced a reversing operation for special vector classes

Analyzed properties over palindromic and antipalindromic vectors

Abstract

In this paper we use a generalized vector product to construct an exterior form $\wedge :(\mathbb{R}^{n}) ^{k}\to \mathbb{R}^{\binom{n}{k}}$, where $\binom{n}{k}=\frac{n!}{(n-k)!k!}$, $k\leq n$. Finally, for $n=k-1$ we introduce the reversing operation to study this generalized vector product over palindromic and antipalindromic vectors.