Abstract
We consider frames in a finite-dimensional Hilbert space, where frames are exactly the spanning sets of the vector space. A factor poset of a frame is defined to be a collection of subsets of , the index set of our vectors, ordered by inclusion so that nonempty is in the factor poset if and only if is a tight frame. We first study when a poset is a factor poset of a frame and then relate the two topics by discussing the connections between the factor posets of frames and their duals. Additionally we discuss duals with regard to -minimization.
Citation
Kileen Berry. Martin S. Copenhaver. Eric Evert. Yeon Hyang Kim. Troy Klingler. Sivaram K. Narayan. Son T. Nghiem. "Factor posets of frames and dual frames in finite dimensions." Involve 9 (2) 237 - 248, 2016. https://doi.org/10.2140/involve.2016.9.237
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