User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)


 * $u \ v \ \mathsf{u} \ \mathsf{v} \ \nu \ \upsilon$

Anyone else have a hard time distinguishing between $u$ and $v$? I would like it to look more like this, does it confuse anyone else? It seems PW doesn't have the upgreek package. --GFauxPas 07:49, 27 January 2012 (EST)


 * Nope. Multiple years of extensive TeX writing and reading have trained my eye. I agree that referenced $v$ looks more distinguished, but imagine it is hard to implement. --Lord_Farin 08:08, 27 January 2012 (EST)

Exponential Definitions
I am discussing the equivalence of the definitions of exponential here:

http://forums.xkcd.com/viewtopic.php?f=17&t=80256

For anyone who has been following my progress or lack thereof on exponent combination laws/log laws etc, feel free to look on. --GFauxPas 16:59, 6 February 2012 (EST)


 * Okay, it looks like $e^{xy} = e^xe^y$ was the hardest one to prove! I was expecting a walk uphill the whole way. Oh, my Linear Algebra book came in the mail, so I guess I'll work on vectors next. And one of these days I'll have to tie up loose ends with Tarski. --GFauxPas 16:57, 10 February 2012 (EST)

elementary matrices
Is this theorem up on PW? I learned it this week in class and it seems like something that should be on PW somewhere, is it? If not, I can try to prove it, maybe, but I wouldn't know what to call it.

Let $\mathbf{X}$ be and $\mathbf{Y}$ be matrices that differ by exactly one elementary row operation.

Then there exists some elementary matrix such that:


 * $\mathbf{EX} = \mathbf{Y}$

--GFauxPas 20:01, 23 February 2012 (EST)


 * Somewhere, I believe, but not in those precise words. --prime mover 01:47, 24 February 2012 (EST)
 * I just looked. We haven't got that in there as it stands, but we do have a sequence of equivalent proofs which gets the user to the point where this approach is leading to. So go ahead and start. --prime mover 01:50, 24 February 2012 (EST)