Definition talk:Magnitude
Actually, having added that see also, I think it would probably make more sense to just merge this into vector length, perhaps under a subheading for physics? --Alec (talk) 12:11, 12 June 2011 (CDT)
- No, better keep it as a separate page. It expresses the context (physics, real-world applications, "how big something is") into which the pure-mathematical idea of "vector length" can be fitted into when applying the latter concept to a real-world idea. --prime mover 13:43, 12 June 2011 (CDT)
Norm or length?
There is a difference between norm and vector length. Damned if I know what it is. Leave as it is until we have worked out what. I think it's that a norm refers to more abstract objects than just vectors of numbers.
In general when it comes to definitions best to leave them as they are unless you either understand it all or have carefully copied it from an authoritative source that you can cite. --prime mover 15:04, 15 November 2011 (CST)
- The problem was I hastily concluded that I did understand it all. Then I rhetorically asked myself what the difference was, and didn't have an answer. That's why I reverted my edit. I was copying from a source, but I realized that the source doesn't really address the distinction. But your advice is noted, thank you. --GFauxPas 15:10, 15 November 2011 (CST)
- Good call. You will note, of course, that I don't always follow my own advice.
- I've taken another look at this example, In this context, i.e. that where the vector consists of real numbers, I believe that the norm and the magnitude are the same. Bear in mind that this is "just" the simple example of vectors as used in "basic" physics: mechanics and applied maths. So the concept of a "norm" is way beyond anything needed here.
- Yes I know that when we get to quantum mechanics and all that malarkey such matters will require advanced techniques, but we already have the concept of the vector space on the general field / ring / what-have-you, but at this level we just need the magnitude. --prime mover 15:52, 15 November 2011 (CST)
- The problem was I hastily concluded that I did understand it all. Then I rhetorically asked myself what the difference was, and didn't have an answer. That's why I reverted my edit. I was copying from a source, but I realized that the source doesn't really address the distinction. But your advice is noted, thank you. --GFauxPas 15:10, 15 November 2011 (CST)
To address the distinction: It might be ambiguous to talk about the norm; many norms on $\R^n$ can be defined (in fact, sometimes more than one is used at once). However, only one of them coincides with the vector length (that is, the Euclidean norm found by the 'Pythagorean' trick). At least, that's what I would say: no reference to back up this statement... --Lord_Farin 16:15, 15 November 2011 (CST)
- I'd discourage it on this page. This page is concerned solely about the magnitude of a vector, as it is used in the context of the simple use of vectors in elementary physics and applied mathematics. As such I would prefer we didn't go anywhere near even mentioning the norm on this page. --prime mover 14:52, 16 November 2011 (CST)