Symmetric Full Spark Frames

Author

Brian Sheehan

Date

5-8-2017

Document Type

Thesis

Abstract

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 S_n 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 S_n admits an orbit which is a full-spark frame if and only if n ≤ 3:

Department

Mathematics

Thesis Comittee

Vignon Oussa (Thesis Director)

Ward Heilman

Laura Gross

Copyright and Permissions

Original document was submitted as an Honors Program requirement. Copyright is held by the author.

Recommended Citation

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