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About: Left Null Space

Module by: Doug Daniels, Steven J. Cox. E-mail the authors

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Name: Left Null Space
ID: m10292
Language: English (en)
Summary: This module defines the left null space, shows an example of what one is, and describes how to find one given an arbitrary matrix.
Subject: Mathematics and Statistics, Science and Technology
Keywords: fundamental theorem, left nullspace, left null space, linear algebra, null, nullspace, space, unique, uniqueness
Document Type: -//CNX//DTD CNXML 0.5 plus MathML//EN
License: Creative Commons Attribution License CC-BY 1.0

Authors: Doug Daniels (, Steven J. Cox (
Copyright Holders: Doug Daniels (, Steven J. Cox (
Maintainers: Doug Daniels (, Mark Barrett (, Steven J. Cox (

Latest version: 2.7 (history)
First publication date: Aug 9, 2001 12:00 am +0000
Last revision to module: Aug 4, 2005 9:01 pm +0000


PDF: m10292_2.7.pdf PDF file, for viewing content offline and printing. Learn more.
XML: m10292_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 Aug 4, 2005 9:01 pm +0000 by Charlet Reedstrom
update to cnxml-0.5

Version: 2.6 Aug 2, 2002 12:00 am +0000 by (Unknown)
auditing this module

Version: 2.5 Jul 19, 2002 12:00 am +0000 by (Unknown)
change the version to 0.4.

Version: 2.4 Jan 9, 2002 12:00 am +0000 by (Unknown)
used Emacs to indent source code

Version: 2.3 Nov 7, 2001 12:00 am +0000 by Brent Hendricks
Sync with DB

Version: 2.2 Aug 24, 2001 12:00 am +0000 by (Unknown)
added some additional left null space information that had been contained in the null space module (m10293)

Version: 2.1 Aug 22, 2001 12:00 am +0000 by (Unknown)
initial version

Version: 2.0 Aug 9, 2001 12:00 am +0000 by (Unknown)
Added initial template for new module m10292

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If you reuse this work elsewhere, in order to comply with the attribution requirements of the license (CC-BY 1.0), you must include

  • the authors' names: Doug Daniels, Steven Cox
  • the title of the work: Left Null Space
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How to Cite and Attribute This Content

The following citation styles comply with the attribution requirements for the license (CC-BY 1.0) of this work:

American Chemical Society (ACS) Style Guide:

Daniels, D.; Cox, S. Left Null Space, OpenStax-CNX Web site., Aug 4, 2005.

American Medical Assocation (AMA) Manual of Style:

Daniels D, Cox S. Left Null Space [OpenStax-CNX Web site]. August 4, 2005. Available at:

American Psychological Assocation (APA) Publication Manual:

Daniels, D., & Cox, S. (2005, August 4). Left Null Space. Retrieved from the OpenStax-CNX Web site:

Chicago Manual of Style (Bibliography):

Daniels, Doug, and Steven Cox. "Left Null Space." OpenStax-CNX. August 4, 2005.

Chicago Manual of Style (Note):

Doug Daniels and Steven Cox, "Left Null Space," OpenStax-CNX, August 4, 2005,

Chicago Manual of Style (Reference, in Author-Date style):

Daniels, D., & Cox, S. 2005. Left Null Space. OpenStax-CNX, August 4, 2005.

Modern Languages Association (MLA) Style Manual:

Daniels, Doug, and Steven Cox. Left Null Space. OpenStax-CNX. 4 Aug. 2005 <>.