A full-spark frame of an n-dimensional vector space is a finite collection of m vectors (m ≥ n) with the following property: every subset of cardinality n of the given collection is a basis for the vector space. In this thesis, we realize the symmetric group Sn as a matrix group of invertible matrices with n2 entries for n > 2: This representation induces a natural linear action on the vector space ℂn and we prove that Sn admits an orbit which is a full-spark frame if and only if n ≤ 3:
Vignon Oussa (Thesis Director)
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Original document was submitted as an Honors Program requirement. Copyright is held by the author.
Sheehan, Brian. (2017). Symmetric Full Spark Frames. In BSU Honors Program Theses and Projects. Item 240. Available at: https://vc.bridgew.edu/honors_proj/240
Copyright © 2017 Brian Sheehan