Diagram vectors and Tight Frame Scaling in Finite Dimensions
Abstract
We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. The diagram vector of a vector in R2 was previously defined using polar coordinates and was used to characterize tight frames in R2 in a geometric fashion. Reformulating the definition of a diagram vector in R2 we provide a natural extension of this notion to Rn and Cn. Using the diagram vectors we give a characterization of tight frames in Rn or Cn. Further we provide a characterization of when a unit-norm frame in Rn or Cn can be scaled to a tight frame. This classification allows us to determine all scaling coefficients that make a unit-norm frame into a tight frame.
Keywords
Cite
@article{arxiv.1303.1159,
title = {Diagram vectors and Tight Frame Scaling in Finite Dimensions},
author = {Martin S. Copenhaver and Yeon Hyang Kim and Cortney Logan and Kyanne Mayfield and Sivaram K. Narayan and Matthew J. Petro and Jonathan Sheperd},
journal= {arXiv preprint arXiv:1303.1159},
year = {2013}
}
Comments
This work was done as a part of the REU program in Summer 2011. Submitted