Construction of Mercedes–Benz Frame in %${\mathbb {R}}^n%$

Abstract In this article, Mercedes–Benz (MB) frame having 3 vectors in %${\mathbb {R}}^2%$ is generalized to the space %${\mathbb {R}}^n%$ with %$n+1%$ vectors through a complete concrete method. A necessary and sufficient condition for a normed tight frame to be an MB frame is given and MB frame is...
Ausführliche Beschreibung

Abstract In this article, Mercedes–Benz (MB) frame having 3 vectors in %${\mathbb {R}}^2%$ is generalized to the space %${\mathbb {R}}^n%$ with %$n+1%$ vectors through a complete concrete method. A necessary and sufficient condition for a normed tight frame to be an MB frame is given and MB frame is explored with the help of diagram vectors. In a new approach, it has been proved that there is no MB frame in %${\mathbb {R}}^n%$ with more than %$n+1%$ vectors and there is always an equiangular tight frame for every %$n \ge 2%$, using MB frame. Ausführliche Beschreibung