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What is odd
about binary Parseval frames?
Zachery J. Baker, Bernhard G. Bodmann, Micah G. Bullock, Samantha N. Branum and Jacob E. McLaney
Vol. 11 (2018), No. 2, 219–233
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Abstract |
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This paper examines the construction and properties of binary Parseval frames. We address two questions: When does a binary Parseval frame have a complementary Parseval frame? Which binary symmetric idempotent matrices are Gram matrices of binary Parseval frames? In contrast to the case of real or complex Parseval frames, the answer to these questions is not always affirmative. The key to our understanding comes from an algorithm that constructs binary orthonormal sequences that span a given subspace, whenever possible. Special regard is given to binary frames whose Gram matrices are circulants. |
Keywords
frames, Parseval frames, binary Parseval frame, binary
cyclic frame, finite-dimensional vector spaces, binary
numbers, orthogonal extension principle, switching
equivalence, Naimark complement, Gram matrices,
Gram–Schmidt orthogonalization
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Mathematical Subject Classification 2010
Primary: 42C15
Secondary: 15A33
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Milestones
Received: 31 August 2015
Revised: 7 March 2016
Accepted: 23 March 2017
Published: 17 September 2017
Communicated by David Royal Larson
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Authors |
| Zachery J. Baker | |
| Department of Mathematics University of Houston Houston, TX United States |
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| Bernhard G. Bodmann | |
| Department of Mathematics University of Houston Houston, TX United States |
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| Micah G. Bullock | |
| Department of Mathematics University of Houston Houston, TX United States |
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| Samantha N. Branum | |
| Department of Mathematics University of Houston Houston, TX United States |
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| Jacob E. McLaney | |
| Department of Mathematics University of Houston Houston, TX United States |
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