Construction of Mercedes–Benz Frame in R n

Abstract

In this article, Mercedes–Benz (MB) frame having 3 vectors in R 2 is generalized to the space 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 R n with more than n+ 1 vectors and there is always an equiangular tight frame for every n? 2 , using MB frame. © 2017, Springer India Pvt. Ltd.