Talk:Elementary Row Operations as Matrix Multiplications

I believe that the redlink "Transform" may be to be something with a more specific name, as there are umpty-finity concepts in maths with the title "transform". In this context what you need to link to is the definition of Matrix Product or whatever it is. --prime mover 01:18, 26 February 2012 (EST)
 * Ideally, the result would also hold for right-multiplication. This would be very useful for Determinant of Matrix Product/Proof 1, as one can take simply left-multiplication for the one, and right-multiplication for the other. --Lord_Farin 03:42, 16 March 2012 (EDT)
 * Actually, I don't know if it does hold for right-multiplication; I honestly didn't think of that. I'll see what I can do. --HumblePi (talk) 12:36, 3 December 2016 (EST)


 * No, it would not hold. Take $\mathbf A = \left[ \begin{array}{ccc}

1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right], \; \mathbf E = \left[ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 1 \end{array}\right]. \; \mathbf E$ is an elementary matrix, then using the conventional matrix multiplication:
 * $\mathbf {AE} = \left[ \begin{array}{ccc}

1 & 2 & 1 \\ 1 & 2 & 1 \\ 1 & 2 & 1 \end{array}\right]$ which is an elementary column operation on A. --HumblePi (talk) 13:08, 3 December 2016 (EST)

Question about sources
Why was the Fraleigh and Beauregard source citation removed? Accidental or deliberate? If deliberate, what was the reason? I have restored it, but in case it was deliberate, can you explain why? --prime mover (talk) 06:28, 3 December 2016 (EST)

Here is your answer
Yes, the removal of the citation was deliberate; let me explain why:

Before I edited this page, it was a stub that had no proof whatsoever, and my edit kind of re-worded the statement of the theorem (it's still the same result though, maybe not as general, but you can still easily apply it to two arbitrary matrices that differ from only one elementary row operation). I've never read this Fraleigh and Beauregard book, and I really didn't feel as though this page uses much (if at all) information from that book, so I removed it.

Now, if you want to keep the source there that's fine. The sources at the end really don't make a difference to me, and I wouldn't want to argue with an administrator (because I don't like arguing with people, and also because I'll lose). By the way, thanks for creating the appropriate pages for the book reference. --HumblePi (talk) 12:27, 3 December 2016 (EST)


 * Oh yes I see what you did. In such circumstances, rather than delete another page to make way for your new stuff (which is effectively what you did), you make a new page to put the different result in place. The fact that the stub had no proof attached to it is not an invitation to remove it.


 * As soon as BBT is over I will revert. --prime mover (talk) 13:57, 3 December 2016 (EST)


 * Hm, I deem the case to be less clear-cut because the two phrasings are obviously equivalent -- if phrased slightly differently. The preferred theorem statement should be put up; the proof is easily amended to follow suit. &mdash; Lord_Farin (talk) 13:59, 3 December 2016 (EST)


 * How about I make the original theorem a corollary of the current one? That way both results are kept and no information would be lost. --HumblePi (talk) 14:05, 3 December 2016 (EST)


 * Yes, that would work. --prime mover (talk) 14:34, 3 December 2016 (EST)