Talk:Row echelon form
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My Precalculus book reports that Row-Echelon form contains the requirement:
"A matrix in row-echelon form has the following properties ... 2. For each row that does not consist entirely of zeros, the first nonzero entry is 1 (Called a leading 1) ..." - PRECALCULUS 7th Edition, Larson & Hostetler
Which is contrary to what is reported in the article.
Which form is correct? Serialized 00:23, 2 December 2006 (UTC)
- Apparently, there isn't universal agreement about this. Some books include that requirement and others don't. A book I have also says this, but someone else here has a book that doesn't say it. See Talk:Gaussian elimination#REF and RREF requirements. Eric119 02:52, 2 December 2006 (UTC)
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- I added a note; I think that the article should mention that there are two slightly differing definitions. -- Jitse Niesen (talk) 13:52, 2 December 2006 (UTC)
[edit] TI-89 Example
Does anyone else think that having the example of "doing" REF on a TI-89 is not appropriate here? There are many different models of calculator and there is no need to single this one out. Such information is more appropriate for the calculator's manual. If we did include it, it would belong in Gaussian elimination, not here. Eric119 05:42, 19 December 2006 (UTC)
- I agree. Besides many calculators, there are also numerical libtaries and computer algebra systems. It makes little sense to explain how to find the REF in all these environments. Hence, I removed the section. -- Jitse Niesen (talk) 11:36, 19 December 2006 (UTC)
[edit] Excess requirement
The article read as follows before I edited it (requirements for RREF):
- All nonzero rows are above any rows of all zeroes.
- The leading coefficient of a row is always to the right of the leading coefficient of the row above it.
- All entries below a leading coefficient, if any, are zeroes.
However, this last requirement is redundant. Take the leading coefficient of any non-zero row. The elements directly below this are either:
- In a zero row, in which case the element is zero, or
- In a nonzero row, in which case that row's leading element is to the right and so the element directly below is also zero.
Thus the third requirement of the above is redundant; it results from the first two.
Unless I've screwed up.
