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Frame theory for
binary vector spaces
Bernhard G. Bodmann, My Le, Letty Reza, Matthew Tobin and Mark Tomforde
Vol. 2 (2009), No. 5, 589–602
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Abstract |
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We develop the theory of frames and Parseval frames for finite-dimensional vector spaces over the binary numbers. This includes characterizations which are similar to frames and Parseval frames for real or complex Hilbert spaces, and the discussion of conceptual differences caused by the lack of a proper inner product on binary vector spaces. We also define switching equivalence for binary frames, and list all equivalence classes of binary Parseval frames in lowest dimensions, excluding cases of trivial redundancy. |
Keywords
frames, binary numbers, Parseval frames, finite-dimensional
vector spaces, binary numbers, binary vector spaces
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Mathematical Subject Classification 2000
Primary: 15A03, 15A33, 42C15
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Milestones
Received: 6 August 2009
Accepted: 12 August 2009
Published: 13 January 2010
Communicated by David Larson
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Authors |
| Bernhard G. Bodmann | |
| Department of Mathematics University of Houston Houston, TX 77204-3008 United States |
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| My Le | |
| Department of Mathematics University of Houston Houston, TX 77204-3008 United States |
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| Letty Reza | |
| Department of Mathematics University of Houston Houston, TX 77204-3008 United States |
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| Matthew Tobin | |
| Department of Mathematics University of Houston Houston, TX 77204-3008 United States |
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| Mark Tomforde | |
| Department of Mathematics University of Houston Houston, TX 77204-3008 United States |
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