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    • Graduate School - MU Theses and Dissertations (MU)
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    • 2009 Dissertations (MU)
    • 2009 MU dissertations - Freely available online
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    Existence and construction of real-valued equiangular tight frames

    Redmond, Daniel Joseph
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    [PDF] short.pdf (54.71Kb)
    [PDF] research.pdf (1.151Mb)
    Date
    2009
    Format
    Thesis
    Metadata
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    Abstract
    This paper presents results on real-valued equiangular tight frames (ETFs) and related topics. Some geometric theorems are developed, and aspects of frame theory are used to gain insight into ETFs. We develop a projection method for analyzing equiangular tight frames that leads to new existence results, and that establishes a link between the geometry of the ETF and the spectrum of the associated Gramian and signature matrices. A new lower bound on the number of frame vectors improves on the best known necessary conditions for existence. We recover the Holmes-Paulsen criterion two different ways, along with additional necessary conditions. We also show that ETFs can be rotated to match a standard position, and that this corresponds to a binary tree structure (partial ordering) of embedded sub-spheres of decreasing dimension. This leads to a new canonical form and an enumerative algorithm to algebraically construct or prove the non-existence of equiangular tight frames.
    URI
    https://hdl.handle.net/10355/6854
    https://doi.org/10.32469/10355/6854
    Degree
    Ph. D.
    Thesis Department
    Mathematics (MU)
    Rights
    OpenAccess.
    This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
    Collections
    • 2009 MU dissertations - Freely available online
    • Mathematics electronic theses and dissertations (MU)

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