Finite normalized tight frames

Frames are interesting because they provide decompositions in applications where bases could be a liability. Tight frames are valuable to ensure fast convergence of such decompositions. Normalized frames guarantee control of the frame elements. Finite frames avoid the subtle and omnipresent approximation problems associated with the truncation of infinite frames. In this paper the theory of finite normalized tight frames (FNTFs) is developed. The main theorem is the characterization of all FNTFs in terms of the minima of a potential energy function, which was designed to measure the total orthogonality of a Bessel sequence. Examples of FNTFs abound, e.g., in R-3 the vertices of the Platonic solids and of a soccer ball are FNTFs.