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About: Orthonormal Basis Expansions

Module by: Michael Haag, Justin Romberg. E-mail the authors

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Name: Orthonormal Basis Expansions
ID: m10760
Language: English (en)
Summary: The module looks at decomposing signals through orthonormal basis expansion to provide an alternative representation. The module presents many examples of solving these problems and looks at them in several spaces and dimensions.
Subject: Mathematics and Statistics
Keywords: basis, basis matrix, coefficient vector, decompose, hilbert, hilbert spaces, orthonormal, orthonormal basis, standard basis
License: Creative Commons Attribution License CC-BY 3.0

Authors: Michael Haag (, Justin Romberg (
Copyright Holders: Michael Haag (, Justin Romberg (
Maintainers: Michael Haag (, Justin Romberg (, Richard Baraniuk (, Mariyah Poonawala (, Prashant Singh (, Matthew Moravec (

Latest version: 2.7 (history)
First publication date: Jul 28, 2002 7:00 pm -0500
Last revision to module: Dec 26, 2013 4:21 pm -0600


PDF: m10760_2.7.pdf PDF file, for viewing content offline and printing. Learn more.
XML: m10760_2.7.cnxml XML that defines the structure and contents of the module, minus any included media files. Can be reimported in the editing interface. Learn more.

Version History

Version: 2.7 Dec 26, 2013 4:21 pm -0600 by Collins Williamson
added moravec as maintainer

Version: 2.6 Jul 29, 2010 2:42 pm -0500 by Collins Williamson
2010 update

Version: 2.5 Oct 1, 2009 10:12 pm -0500 by Richard Baraniuk
added google analytics tracking code

Version: 2.4 Jun 24, 2005 10:00 am -0500 by Charlet Reedstrom
update to cnxml-0.5, fix typo, wrap msub in ci

Version: 2.3 Jul 9, 2003 2:05 pm -0500 by Charlet Reedstrom

Version: 2.2 Jul 31, 2002 12:00 am -0500 by (Unknown)
Added vertical ellipses to matrices of vectors to show it is not just a row matrix.

Version: 2.1 Jul 30, 2002 12:00 am -0500 by (Unknown)
New module created.  Verified printing.

Version: 2.0 Jul 29, 2002 12:00 am -0500 by (Unknown)
Added initial template for new module m10760

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Haag, M.; Romberg, J. Orthonormal Basis Expansions, OpenStax-CNX Web site., Dec 26, 2013.

American Medical Assocation (AMA) Manual of Style:

Haag M, Romberg J. Orthonormal Basis Expansions [OpenStax-CNX Web site]. December 26, 2013. Available at:

American Psychological Assocation (APA) Publication Manual:

Haag, M., & Romberg, J. (2013, December 26). Orthonormal Basis Expansions. Retrieved from the OpenStax-CNX Web site:

Chicago Manual of Style (Bibliography):

Haag, Michael, and Justin Romberg. "Orthonormal Basis Expansions." OpenStax-CNX. December 26, 2013.

Chicago Manual of Style (Note):

Michael Haag and Justin Romberg, "Orthonormal Basis Expansions," OpenStax-CNX, December 26, 2013,

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Haag, M., & Romberg, J. 2013. Orthonormal Basis Expansions. OpenStax-CNX, December 26, 2013.

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Haag, Michael, and Justin Romberg. Orthonormal Basis Expansions. OpenStax-CNX. 26 Dec. 2013 <>.