Vol. 2, No. 5, 2009

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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
Abstract

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
Mathematical Subject Classification 2000
Primary: 15A03, 15A33, 42C15
Milestones
Received: 6 August 2009
Accepted: 12 August 2009
Published: 13 January 2010

Communicated by David Larson
Authors
Bernhard G. Bodmann
Department of Mathematics
University of Houston
Houston, TX 77204-3008
United States
My Le
Department of Mathematics
University of Houston
Houston, TX 77204-3008
United States
Letty Reza
Department of Mathematics
University of Houston
Houston, TX 77204-3008
United States
Matthew Tobin
Department of Mathematics
University of Houston
Houston, TX 77204-3008
United States
Mark Tomforde
Department of Mathematics
University of Houston
Houston, TX 77204-3008
United States