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Talk:Elementary matrix

From Encyclopedia of Mathematics
Revision as of 18:13, 20 March 2015 by Boris Tsirelson (talk | contribs) (thank you)
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Issue

This definition excludes the row-switching elementary matrix[1]:


16c94d719d94fe7b7a397a59d781be2b.png

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

  1. ↑ Wikipeida - Row-switching transformations
  2. ↑ Wikipedia - Elementary matrix


--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
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