Wikipedia:Reference desk/Archives/Mathematics/2014 March 4

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March 4

orthogonal component

Please pardon the low level of this question. Given two vectors u,v (in R3) how would you get the magnitude of the component of v that is perpendicular to u? The approaches that come to my mind are rather roundabout and I can't help thinking there must be a more direct way – perhaps one that I learned in my youth but never had occasion to use! —Tamfang (talk) 05:03, 4 March 2014 (UTC)

I would think there are infinitely many orthogonal components (in R³) unless you restrict your desired component to be in the same plane as u and v, or equivalently, such that the addition of this "orthogonal" component to the component along u is equal to v. If you do that, then we can use the Pythagorean theorem using the magnitude of v and the component of v along u and obtain the magnitude of that component. Or geometrically, multiply |v| by the sine of the angle between u and v.--Jasper Deng (talk) 05:14, 4 March 2014 (UTC)

Both of those begin with normalizing at least one of the vectors, which I was rather hoping I might not need to do (given that the project I have in mind would involve finding this quantity many thousands of times). —Tamfang (talk) 05:50, 4 March 2014 (UTC)

I've also noticed that perhaps (this works in R³ and R⁷ only, interestingly) you could take a cross product and then divide the magnitude of that by the norm of u. But then again, this also relies on finding magnitudes of the vector, albeit only u in this case.--Jasper Deng (talk) 06:24, 4 March 2014 (UTC)

This is called the vector rejection of u from v. See the article for a number of different approaches to computing it. --Mark viking (talk) 06:18, 4 March 2014 (UTC)

Thanks! What a pleasure to learn a new word.

It occurred to me later that (for my purpose) I don't really need the magnitude of the rejection: its biggest Cartesian element ought to do. —Tamfang (talk) 00:03, 5 March 2014 (UTC)

Mathematical proof as a source

Does a fully valid mathematical proof count as a proper source for citation purposes? 180.200.151.199 (talk) 06:45, 4 March 2014 (UTC)

Do you mean whether you can use a mathematical proof that you yourself constructed? Wikipedia:No original research sets a limit on that. Naturally, a proof such as the fallacy relying on dividing by 0 is obviously not a reliable source for anything in mathematics.--Jasper Deng (talk) 06:57, 4 March 2014 (UTC)

It's also not a proof, it just looks like one ;-). --Stephan Schulz (talk) 07:25, 4 March 2014 (UTC)

Not in Wikipedia. In Wikipedia what is needed is a WP:Reliable source and one's own proof is counted as WP:Original research. It doesn't matter how good the proof is. Wikipedia is an encyclopaedia and tries to summarize notable things that are out there already. Dmcq (talk) 08:50, 4 March 2014 (UTC)

However, if you have constructed a valid proof that isn't cited anywhere else, you may get an article out of it :) OldTimeNESter (talk) 13:10, 4 March 2014 (UTC)

See discussion here: Wikipedia_talk:WikiProject_Mathematics#Insertion_of_Original_research_in_several_articles YohanN7 (talk) 18:24, 4 March 2014 (UTC)

There is the business also that Wikipedia shouldn't normally be providing proofs anyway. A short explanation or outline might be fine but actual proofs should normally be left to cited references. An exception is where the proof itself has achieved notability. Dmcq (talk) 18:34, 4 March 2014 (UTC)

The rules we have here on Wikipedia are flexible per WP:IAR. One has to consider here that the rules we have have evolved since the creation of Wikipedia to deal with the typical editing conflicts, like the Israeli Palestinian conflict; the pros and cons of including a math proof and how to do that isn't such an issue that the rules like WP:NOR or WP:SYNTH have been fine tuned to deal with. Count Iblis (talk) 13:40, 6 March 2014 (UTC)