A note on Euclidean spaces $\mathbb{R}^n$ and $n$-normed spaces

Idris, Mochammad

Hilbert Journal of Mathematical Analysis
Vol. 1 No. 2 (2023): Hilbert J. Math. Anal.

This article gives us a relation between Euclidean space $\mathbb{R}^n$ and a subspace of $X$ (an $n$-normed space) using properties of determinant of square matrices. Some functionals will be investigated on these spaces. Furthermore, we obtain definition of inner product and $m$-inner product with $m<n$ on the subspace of $X$.