Difference between revisions of "Talk:Elementary matrix"
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Neo razgriz (talk | contribs) |
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--[[User:Neo razgriz|Neo razgriz]] ([[User talk:Neo razgriz|talk]]) 14:24, 20 March 2015 (CET) | --[[User:Neo razgriz|Neo razgriz]] ([[User talk:Neo razgriz|talk]]) 14:24, 20 March 2015 (CET) | ||
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| + | : Thank you. Probably you are right. But, being not an algebraist, I am not sure: maybe different (non-equivalent) definitions are in use? [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 19:13, 20 March 2015 (CET) | ||
Revision as of 18:13, 20 March 2015
Issue
This definition excludes the row-switching elementary matrix[1]:
Proof
The matrix above (marked T) has more than one off-diagonal element added to it.
In addition, at least one diagonal element has been modified.
Therefore, by the definition on the Elementary matrix page, T is not an elementary matrix.
Alternate definition
In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation.[2]
References
--Neo razgriz (talk) 14:24, 20 March 2015 (CET)
- Thank you. Probably you are right. But, being not an algebraist, I am not sure: maybe different (non-equivalent) definitions are in use? Boris Tsirelson (talk) 19:13, 20 March 2015 (CET)
How to Cite This Entry:
Elementary matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Elementary_matrix&oldid=36335
Elementary matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Elementary_matrix&oldid=36335