On matrices of closed balls

Abstract

Motivated by interval mathematics, the research on an arithmetic for closed balls in $\mathbb{R}^n$ is continued.
In this sense, more algebraic properties of certain operations on closed balls in $\mathbb{R}^n$, some of which related either to the Hadamard product of vectors or to the 2-fold vector cross product when $n \in \{3, 7\}$, are established.
Furthermore, an arithmetic for matrices of closed balls is pursued, and algebraic properties of certain operations on matrices of closed balls, some related to the mentioned operations on closed balls, are studied.
In addition, metric properties for closed balls in $\mathbb{R}^n$ as well as for matrices of closed balls, convergence in particular, are also presented.