|WikiProject Mathematics||(Rated C-class, Mid-importance)|
Significance of unit vector
@ Charles Matthews: You are of course right if you say that the unit vector is not an identity of the multiplication, however it should be mentioned that it plays such a important role as does the null vector (which seems superflous for newcomers) because the unit vector is required to satisfy the rules of a mathemtical group and thus makes it an algebra in the first place. The same goes for the null vector. I would really appreciate it, if you could add this to both entries in terms that satisfy the otherwise strong mathemtical context, and i suppose you as a mathematican could do so best.--Slicky 11:40, Sep 17, 2004 (UTC)
Sorry, this really doesn't add up. There is no such thing as the unit vector, for one thing.
Charles Matthews 11:57, 17 Sep 2004 (UTC)
I am sorry i confused something. My bad. However regarding the null vector is should be mentioned that vector1 + null-vector = vector1 (thus the null-vector is the neutral element for the vector '+'-operation in a standard vector space). And because of that a group can be build (homogen, associative, neutral element, inverse element, commutative -> thus it is even abelian). Am I still mislead? I just deem it important to mention, because at first sight the null vector would seem a bit redundant.--Slicky 19:06, Sep 17, 2004 (UTC)
Uhm,just saw it, i dunno what's gotten into me today. Its just that i am tired and a bit in a messy state. I apologize for that.
Good page. Clear and understandable, even to those without a doctorate in math. My interest is primarily in the use of coordinate cosines to describe ridgid body rotations in 3 dimensional space and the derivation of quaternions as used for the same purpose. SEIBasaurus.
Request for Expansion
I think it would be benificial to include unit vectors in the different coordinate systems (cylindrical, spherical, etc.). I'm not sure if this would be better suited for the coordinates page or not.
I think having a reference of curvilinear unit vectors and their properties (e.g. derivatives) would be especially helpful for those applying them to fields like electrodynamics and fluid mechanics.
I don't have a Ph.D, but I'm fairly fluent in vector calculus and could probably contribute more to the page. I just wanted to get some opinions and feedback first. RyanC. 19:46, 27 April 2006 (UTC)
Alright, I just ended up expanding the article myself. If anyone else frequents this page, let me know what you think.RyanC. 04:01, 1 May 2006 (UTC)
I took out the references to E&M when I rewrote since nothing here is specific to the field (pun unintentional). Lemme know (or just rewrite it better than I did) if I'm stepping on your toes too much. Eldereft 22:15, 26 May 2006 (UTC)
Good edits, I kind of got lazy and didn't bother to define the ranges of the variables. Looks good. I put the physics references in there because the only texts I've seen these coordinate systems used in were E&M and fluid dynamics. I haven't seen a math book on vector calculus that went into much depth at all about rotating coordinate systems. Then again I haven't read very many advanced texts on the subject. I've always been under the assumption that mathematicians worked primarily in Cartesian coordinates. Not really arguing the edits, mostly looking for feedback. Thanks. RyanC. 08:24, 30 May 2006 (UTC)
I'm actually kinda missing the notation (or , , etc). Especially in physics where changes of coordinate system and the use of i and j for the imaginary unit (and/or current) can cause ambuguity, this is often used. I might add this myself (but feedback is appreciated of course) -- what I was actually wondering about is if it's not possible to make a dotless i, j, k to put the hat over. --CompuChip 09:54, 24 November 2006 (UTC)
- On a related subject, I've seen in some (physics) books a-notation, where say the unit vector corresponding to the vector r becomes . Is there any information on this subject somewhere? I can't find it in the article. Eudoxie (talk) 21:22, 13 February 2008 (UTC)
While I understand the geometrical meaning of and , I don't understand = .
and relate to the length of their components, but an angle does not have a length. seems to be "90° ahead" of the angle it is describing. So what is it good for? --Abdull 10:10, 12 September 2007 (UTC)
- Answer to myself: all three vectors form a orthogonal system. --Abdull 10:51, 12 September 2007 (UTC)
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Unit Vector vs. Coordinate
Expanding the unit vector concept
The term unit vector gets used quite widely in contexts with an indefinite or even degenerate metric tensor, and then gets linked here. It seems to me that this generalized use should be defined in this article. I'm not sure how this generalization is normally done, but it seems to me that a
seminorm √|(v⋅v)| must be defined, and this scalar used to normalize a vector. Unit vectors then come in two varieties: those that square to +1, and those that square to −1 (though it may get more complicated by contexts using non-real scalars and sesquilinear forms). Comment? — Quondum 10:53, 5 September 2012 (UTC)
- The generalization should be added. I'll look for sources and may come back later... (unless someone rewrites the article before then). Maschen (talk) 13:14, 5 September 2012 (UTC)
- Cool. I see seminorm is the wrong term (since that is subadditive, but what we're looking for isn't. The closest that I can find is Minkowski norm.