Talk:Norm (mathematics)

message: Why is the length of a vector called a norm? And who was the first person to use this word in this meaning?
In ordinary language, "normal" means something usual without any special property.
In geometry, however, normal means something special, namely perpendicular (or orthogonal).
This is a surprise for me.
And why do we call the length of a vector "a norm of the vector"?
Pokyrek (talk) 07:59, 26 February 2019 (UTC)
thread_title: The origin of this meaning of the word norm?

message: Does anyone know what the modulus of an element of an arbitrary field is? Does the notion of modulus exist in every field?
:You can't do it for all fields. The article as it stands right now is wrong. AxelBoldt 19:28, 22 Apr 2005 (UTC)
thread_title: modulus of an element of an arbitrary field

message: I don't know what the || notation means.  From context, I think I get that it is analagous to absolute value or cardinality, but for vectors.  Will someone please add something explictly introducing the || notation either here or on it's own page?
Kal Culus
I do not understand your question. || is a function on a vector space. We write |.| to indicate the function has to be feed a vector. We could also write f(x), with f the norm and x an element of the vector space V. The properties of the norm function are given in the article. I do not know how to make this more explicit in the article. MathMartin 13:33, 29 Oct 2004 (UTC)
thread_title:  Link to an explanation of the || notation? 

message: This article defines norms for any field F, but there is a problem with axiom 2 since it relies on a real-valued function |a| defined in the field.  What does that mean for a finite field, for example? --Zero 06:28, 23 Apr 2005 (UTC)
replies: text: I really don't know whether it's possible to make the definition of norm general enough for more fields.  I guess for the norm to exist, we need some kind of map from our base field to the reals which will itself satisfy the axioms of a norm.  a sort of subadditive field homomorphism to R.  Do such things exist for finite fields?  I have no idea.  Certainly I've never seen anything like that. -Lethe | Talk 17:25, July 11, 2005 (UTC)
I agree something does not make sense.  If F=C are the complex numbers, then axiom 2 has no meaning, as C is not an ordered field, so we cant say that p(u+v) <= p(u) + p(v)  — Preceding unsigned comment added by 186.18.76.220 (talk) 01:53, 28 September 2011 (UTC)
thread_title:  Any field? 

message: Somehow I seem to remember there being a person's name associated with the process of turning a seminorm into a norm by modding out by the vectors of norm zero, in just the same way that you turn the space of Lebesgue square integrable functions into a Banach space by identifying functions that agree almost everywhere.  I came to wikipedia to look up this name, but couldn't find it.  Am I imagining this? -Lethe | Talk 02:46, July 11, 2005 (UTC)
::It works exactly like for Lebesgue case (which is in fact a special case of this): You just consider the quotient space modulo the subspace of vectors of zero seminorm, on which the (induced) seminorm (the seminorm is independent of the representative of a class) is a norm. (But I don't know whose name could be associated to this -- maybe you think of the associated Hausdorff space, where this is a special case of.) — MFH:Talk 21:59, 28 February 2006 (UTC)
replies: text: For a finite field, I think there is only one.  Define |x|=1 if x is not zero, and |0|=0.  Not terribly useful!  --Zero 17:02, 13 July 2005 (UTC)
thread_title:  turning a seminorm into a norm 

message: In my Finite Element Analysis course, I keep running into the L2 norm,
:\|u-u_h\|_0 = \sqrt{\int_a^b |u-u_h|^2\,dx}
and the "energy norm" (which apparently, for most solid mechanics applications, denotes energy):
:\|u-u_h\|_m = \sqrt{\int_a^b\sum_{i=0}^m \left| \frac{d^i u}{dx^i} - \frac{d^i u_h}{dx^i}\right|^2\,dx}
Can someone who knows more than I on the subject add information on these? —BenFrantzDale 03:49, 27 September 2005 (UTC)
replies: text: In the section p-norm in this article, there is a reference to Lp space where that kind of norms are discussed. Oleg Alexandrov 05:16, 27 September 2005 (UTC)
replies: text:  That article is not very well suited for explaining the L2 norm.  IMO it's worth having a separate article, as it's used quite commonly.  Info from Mathworld could be adapted. 142.103.235.1 19:30, 21 February 2006 (UTC)
replies: text:  You want L2 norm, then visit the article on L2 norm. :) Oleg Alexandrov (talk) 00:30, 22 February 2006 (UTC)
thread_title:  L<sub>2</sub> and energy norms? 

message: We need to generalize max to sup for infinity norm.  MathStatWoman 09:26, 22 January 2006 (UTC)
replies: text: I don't think that's right.  If a sequence doesn't have a largest element, then its l-∞ norm is not finite. -lethe talk 10:24, 22 January 2006 (UTC)

text: Unless your "Oh never mind" is something I'm missing, the wording is ambiguous. A norm is always a scalar, so if you take "dimension" in the number-of-components sense, then the phrasing is wrong. Taking the other meaning -- edge length -- the article is just wrong. I just rephrased it. —Ben FrantzDale (talk) 10:52, 16 October 2008 (UTC)
thread_title:  infinity norm 

message: If we have an article entitled "Norm(mathematics)", should we not include the concepts of Banach spaces, norms based on the general Lebesgue integrals as well as countable sums, and sup norms?  To quote from Banach spaces: "The Banach space l∞ consists of all bounded sequences of elements in K; the norm of such a sequence is defined to be the supremum of the absolute values of the sequence's members." MathStatWoman 13:04, 22 January 2006 (UTC)
replies: text:  If you want to add more stuff to this article, please go ahead. But don't do much integration work by removing stuff from other articles. That seldom works. Oleg Alexandrov (talk) 17:30, 22 January 2006 (UTC)
replies: text:  We are on the same wavelenth. When I hear people taking big plans about reorganizing things I assume the worst. :) Happily not this time. :) Oleg Alexandrov (talk) 01:10, 23 January 2006 (UTC)

text: Go ahead. :) Oleg Alexandrov (talk) 02:40, 24 January 2006 (UTC)
thread_title: More about norms

message: I found a weak norm being used at http://www.sm.luth.se/~johanb/applmath/chap3en/part3.htm. Should this be in the main article? --Sunnyside 10:40, 9 February 2006 (UTC)
replies: text: I guess one needs to have a section in this article discussing norms on function spaces. That seems to be missing now. Then, that norm would be most welcome, but I never heard it being called weak norm though, some references for that (except the web page) would be needed. Oleg Alexandrov (talk) 23:02, 9 February 2006 (UTC)
thread_title:  Weak norms 

message: Perhaps there is a L_(-infinity), with a unit circle of a cross (0 width)? —The preceding unsigned comment was added by 67.183.154.231 (talk) 04:01, 5 December 2006 (UTC)
replies: text: what quite sure what you mean by inf there. if you consider the Lp norm on say R2, with p < 1. this is not really a norm since the unit sphere is not convex. as p tends to 0, the unit circle probably looks more and more like a cross. Mct mht 09:03, 5 December 2006 (UTC)
thread_title:  L_-inf 

message: Resolved
Regarding edits.  I didn't confuse hamming distance with the taxicab norm.  My interpretation is not incorrect, hamming distance and 1-norm are equivalent reductions(HAMMING ≤ 1-norm).  You could consider the hamming distance to be the 1-norm of the binary vertex representing the difference between two vertices on a Hypercube graph.  (hamming(A, B) = "1-norm"(A-B) or "1-norm"(A⊕B)).  In addition Hamming_distance states "and the Hamming distance of the strings is equivalent to the Manhattan_distance between the vertices." and you can see that "Manhattan distance" is redirected to Taxicab_geometry.  These two concepts are very similar and indeed they are reducibly equivalent.  --ANONYMOUS COWARD0xC0DE 10:01, 3 January 2007 (UTC)
replies: text: you're right, on the hypercube the hamming distance and the l1 distance are the same.  however, the rest of the article is using vector spaces over the reals as examples.  i think introducing the hamming distance at that point in the article confuses the reader.  perhaps you could make a breakout section on norms for vector spaces over other fields ({0,1} in the case of the hypercube).  Lunch 19:31, 3 January 2007 (UTC)
replies: text: Meh I thought I would add it, but it is a little bit off topic I agree.  --ANONYMOUS COWARD0xC0DE 00:53, 10 January 2007 (UTC)
thread_title:  Taxicab, 1-norm, and hypercubes. 

message: In the part where it talks about how every seminormed vector space induces a normed vector space V/W, I don't understand the formula (||W+v|| = p(v)) that is given for the induced norm on V/W.  For one thing, what does it means to add the vector space W to the vector v?
:W + v denotes an element of the quotient space V/W; it's the equivalence class [v]. say we're in R^3 and W is a 2-d subspace, then W + v is the affine plane obtained by translating W by v. we should also check that the definition (||W+v|| = p(v)) is independent of the representative v. Mct mht 03:49, 6 July 2007 (UTC)
thread_title:  Don't understand norm of ''W'' + '''v''' 

message: There are a lot of names for various norms. We need some cleanup to clarify this. There's "Euclidean norm", L2, taxicab, etc. It should be made clear in the introduction which of these is which and some of the redirects need to be looked into. For example L1 norm redirects neither here nor to Lp space. —Ben FrantzDale 00:53, 11 October 2007 (UTC)
thread_title:  Minor cleanup needed 

message: The L1 circle is described as a rhomboid when it is a square.  Any objections to fixing this?  --Vaughan Pratt (talk) 19:22, 26 June 2008 (UTC)
thread_title: Rhomboid &rarr; square? 

message: Note that in some contexts, the term "semi" is used when the triangle equality doesn't hold. In some cases, it is used synonym to "pseudo" (non-zero vectors of length 0 allowed). However these don't necessarily fall together (at least not for distance functions), do they?
E.g. euclidean-like distance in a torus space (using the shortest path on the torus) doesn't fulfill the triangle equality, but the condition  d(x,x)==0 <=> x=x  holds.
Unfortunately these terms are totally mixed up in all the related articles here on wikipedia.
138.246.7.155 (talk) 16:35, 24 November 2008 (UTC)
thread_title:  Semi-* vs. Pseudo-* 

message: The article defines the p-norm of a vector x in the usual way -- as the pth root of the sum of the pth powers of its components.
Two lines later it states, referring to this definition:
"This formula is also valid for 0 < p < 1, but the resulting function does not define a norm, because it violates the triangle inequality."
Agreed that it violates the triangle inequality.  But I do not understand what "the formula is also valid" means here.  Simply that the formula can be evaluated, i.e., that it makes mathematical sense?  In that case, why exclude negative values of p ?  (And why not also mention what happens when p -> 0 and when p -> -oo ?)Daqu (talk) 06:55, 26 December 2008 (UTC)
thread_title: The p-norm formula for 0 < p < 1 is "also valid" in what sense???

message: I could not find an article or any mention of the following norm,
:\|x\|_A=(Ax,x),
where A is positive definite matrix, and () is the inner product. Does this norm have a name in English? (Igny (talk) 15:38, 18 January 2009 (UTC)
replies: text: That's not a norm. Do you mean \sqrt{(Ax,x)}? If so, I don't know a name for it. Algebraist 20:51, 18 January 2009 (UTC)
replies: text: Err, yes that is what I meant. I just thought to improve the expression as well as provide a relevant link for the last formula in the GMM. (Igny (talk) 03:07, 19 January 2009 (UTC)

text:  It is sometimes called the Energy norm. I think it is in my Springer Functional Analysis graduate text. —Ben FrantzDale (talk) 21:51, 19 January 2009 (UTC)
thread_title:  Weighted norm 

message: To add to the overall clarification in the examples section, it might be a  good idea to add some numerical examples in with all of the symbolic examples.  —Preceding unsigned comment added by 132.235.19.87 (talk) 13:03, 28 April 2009 (UTC)
thread_title:  Examples 

message: regarding this in the introduction: The Euclidean norm assigns to each vector the length of its arrow. Because of this, the Euclidean norm is often known as the magnitude. 
Isn't the "length" of the arrow determined by the norm? Is there anything really more fundamental about "length"?  The statement seems circular. 76.175.72.51 (talk) 16:26, 20 September 2009 (UTC)
replies: text: It is trying to be friendly to readers who already know what "length" means but came here to find out what "norm" means.  So the point is "you already know one norm under the name 'length', it is called the Euclidean norm".  Zerotalk 01:08, 21 September 2009 (UTC)
thread_title: Length and the norm

message: I find it instructive to link to related concepts that answer the question "What if you remove axioms?". In particular, I am curious about what happens when you drop axiom 1 from the definition of norm? Do you get a function that defines a metric? I think so, but am not sure... 
Metric requires:
:For all x, y, z in X, this function is required to satisfy the following axioms:
:# d(x, y) ≥ 0     (non-negativity)
:# d(x, y) = 0   if and only if   x = y     (identity of indiscernibles. Note that condition 1 and 2 together produce positive definiteness)
:# d(x, y) = d(y, x)      (symmetry)
:# d(x, z) ≤ d(x, y) + d(y, z)      (subadditivity / triangle inequality).
:The first condition is implied by the others. 
Norm requires:
:For all a in F and all u and v in V,
:# p(a v) = |a| p(v), (positive homogeneity or positive scalability)
:# p(u + v) ≤ p(u) + p(v) (triangle inequality or subadditivity). 
:# p(v) ≥ 0, with  p(v) = 0 if and only if v is the zero vector (positive definiteness). 
:A simple consequence of the first two axioms, positive homogeneity and the triangle inequality, is p(0) = 0 and thus
:: p(v) ≥ 0 (positivity).
The thing that throws me is the note at the end of the "norm" axiom. It seems that criterion 3 is prescribing positive-definiteness. But the note says positivity and non-degeneracy (in the sense that p(x)=0\,\Rightarrow\, x=0) is implied by the first two "norm" axioms. If so, then all axiom 3 adds is definiteness. Is that right?
If all of axiom 3 is required, then dropping axiom 1 seems to leave you with a function, p, still defining a metric, d(x,y) = p(x-y). However, if criterion 3 is really a note, implied by axioms 1 and 2, but not an axiom defining "norm", then criterion 3 would fail if we remove axiom 1 and so "a norm without criterion 1" wouldn't define a metric without criterion 3.
Why is axiom 3 so long if much of it is implied by axioms 1 and 2?
Which axioms can be removed from "norm" to still get something that defines a metric? —Ben FrantzDale (talk) 15:13, 28 January 2010 (UTC)
thread_title:  "Almost norm" 

message: One of the key properties of norms is that they are all equivalent up to constant factors.  In particular, if \Vert x \Vert_a and \Vert x \Vert_b are two norms, then there exist some positive constants C1 and C2 such that:
:C_1 \Vert x \Vert_b \leq \Vert x \Vert_a \leq C_2 \Vert x \Vert_b
for all x in a vector space (for the same constants).  As a consequence, it doesn't matter what norm you pick if you don't care about constant factors, which is very convenient for proving lots of asymptotic bounds, talking about stability of algorithms, etcetera.  This is discussed e.g. in Trefethen and Bau, Numerical Linear Algebra.
(At least, this is true for finite-dimensional vector spaces; I'm not sure about the infinite-dimensional case.)
(Proof in brief: prove that any norm is continuous, reduce to considering the unit ball by dividing by \Vert x \Vert_b, then invoke fact that continuous functions achieve their maxima and minima on a compact set to obtain C1 and C2.)
Anyway, it seems like this should be mentioned somewhere.
— Steven G. Johnson (talk) 02:58, 15 March 2010 (UTC)
replies: text: Look in the section "Properties".  Zerotalk 03:59, 15 March 2010 (UTC)
thread_title:  equivalence of norms missing from article 

message: It's possibly a simple oversight, but complex numbers all have norms, or at least that was what Euler called \sqrt{x^2 +y^2} for the complex number x + iy.  And yet this article has no section on complex number norms. The complex number wiki has a section on how to compute this value for complex numbers, but doesn't CALL it a "norm," but rather modulus, absolute value, or magnitude. But if a complex number is considered a vector, then obviously its magnitude is the norm. Has the Euler usage entirely gone by the wayside?  It's not obvious how to compute a complex norm, as you multiply by the complex conjugate, which means you essentially disregard the quantity i. If you didn't, and included it, you'd get a different kind of norm (the Minkowski norm). Is there something in the terminology here that I'm missing? Obviously I'm no mathematician. SBHarris 01:55, 8 April 2010 (UTC)
replies: text: Nevermind, I found my answer in the article on absolute value. The Euclidian norm of a complex number is indeed the absolute value of it, if the complex plane is identified with the Euclidean plane R2. I'll stick that in here, someplace.SBHarris 22:16, 20 April 2010 (UTC)
thread_title:  Norm of a complex number 

message: Regarding this edit  I don't believe 0 is an imaginary number, so the imaginary numbers are not an abelian group. much less a vector space. — Carl (CBM · talk) 10:44, 27 October 2010 (UTC)
replies: text: Arguable, but I suppose the ambiguity doesn't help.  I'll revert, although the real numbers really aren't a good example of a vector space over a field, if the field is also the real numbers.  — Arthur Rubin  (talk) 14:17, 27 October 2010 (UTC)
thread_title:  Imaginary numbers a vector space? 

message: A moment ago I wrote in an edit summary
: an n-sphere is the surface of an (n-1)-ball.
And after clicking, of course, I noticed that I meant (n+1)-ball.  Oh well. —Tamfang (talk) 21:25, 11 July 2011 (UTC)
thread_title:  plus or minus 

message: User:Rheyik recently added:
: The one norm is simply the maximum column sum of absolute values.
: The infinity norm is simply the maximum row sum of absolute values.
Uh, what?  I guess these definitions concern something fancier than the plain old vectors that appear to be the context of the rest of the article. —Tamfang (talk) 01:20, 12 December 2011 (UTC)
replies: text: I haven't checked the article, but those are quick ways to calculate the operator norm of a matrix acting on vectors with the p-norm for p=1 and p=∞.  |A| = max( |Av|/|v| : v ≠ 0 ). JackSchmidt (talk) 17:38, 12 December 2011 (UTC)
thread_title:  row sum? column sum? 

message: Why does Pseudonorm redirect to this page, when the page doesn't mention "Pseudonorm" anywhere?  I have seen pseudonorm used in the sense of the Hamming-distance from 0, but there maybe other conventions. It would be nice to mention it, even if only to say that there is no consensus on the terminology. Lavaka (talk) 14:35, 20 April 2012 (UTC)
thread_title:  Pseudonorm 

message: I improved the Notation section and put it after Definition section which is a more logical place for it.
I removed the claim that set cardinality is a norm and should be noted by double vertical bars because I cannot see how sets would make up a normed vector space (if there is a natural way to do it, it would be interesting to know) and single-bar notation is also much more common for cardinality.
I removed the claim that denoting norm by single bars is generally discouraged. Actually, the the only case where I have encountered the single-bar notation is the case of Euclidean spaces, and for them, such usage is widespread, so a statement that it has been discouraged should be backed up by an authoritative source. I also removed the suggestion of denoting matrix norm with double vertical line since matrix spaces are special cases of vector spaces and I haven't seen their norms being denoted otherwise. (I personally do not see a problem with norm being confused with absolute value in case of Euclidean spaces, since the Euclidean norm in 1-dimensional space is exactly the absolute value. For matrices, I would rather blame the notation of determinant with single bars as a source of confusion, since for the usual matrix norms, the norm of a 1-by-1 matrix is the absolute value of its only element but it may differ from the determinant of the matrix by sign.)
If someone knows some sources where norms on generic vector spaces or matrix spaces or some other specific spaces are denoted by single bars and can find a source that such notation is discouraged, then such suggestions can be added back to the Notation section. 
Jaan Vajakas (talk) 16:30, 14 September 2012 (UTC)
thread_title:  Notation 

message: I removed the claim "Although every vector space is seminormed (e.g., with the trivial seminorm in the Examples section below), it may not be normed." since it is not true (for vector spaces over subfields of \mathbb C). Indeed, for a field F, algebraic vector spaces over F are characterized by the cardinalities of their Hamel bases. For a vector space V Hamel basis e_\alpha, \alpha \in A, where A is an arbitrary (possibly infinite) set, we can consider any p-norm w. r. t. the basis, e. g. the 1-norm \left\|\sum_{i=1}^k a_i e_{\alpha_i}\right\| = \sum_{i=1}^k |a_i|. Jaan Vajakas (talk) 17:07, 14 September 2012 (UTC)
thread_title:  All algebraic vector spaces over subfields of <math>\mathbb C</math> are normable 

message: I removed references to a "B-norm" (which as far as I can tell just means "norm") and attempted to clarify the meaning of "F-norm" in this article. The definition, from Rolewicz's book is the one I gave in the article, i.e. it is just x \mapsto d(x,0) where d is a distance in an F-space. That's not very satisfying and Rolewicz also gives some intrinsic conditions, namely \lVert \cdot \rVert is an "F-norm" if: \lVert x \rVert = 0 iff x=0; \lVert -x\rVert = \lVert x \rVert; and the triangle inequality holds.
I didn't feel like writing these out in the article, largely because I am unsure that this F-norm business belongs in here. Maybe it should go onto the F-space article, but I'm not really qualified to work out whether it is significant or interesting.
While tidying I also tried to make the language a bit less judgmental. I don't know what "some engineers" means - I think that some mathematicians also call things norms when they aren't norms. Anyway. 130.88.123.107 (talk) 14:20, 24 November 2015 (UTC)
thread_title:  B-norm/F-norm 

message: The article doesn't mention the process of normalization, although it would seem to be relevant.  75.139.254.117 (talk) 05:15, 28 December 2016 (UTC)
thread_title:  Normalization? 

message: A discussion is taking place to address the redirect :L2 norm. The discussion will occur at Wikipedia:Redirects for discussion/Log/2020 June 11#L2 norm until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  1234qwer1234qwer4 (talk) 11:38, 11 June 2020 (UTC)
thread_title:  "L2 norm" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: A discussion is taking place to address the redirect :L2 norm. The discussion will occur at Wikipedia:Redirects for discussion/Log/2020 June 24#L2 norm until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  1234qwer1234qwer4 (talk) 14:50, 24 June 2020 (UTC)
thread_title:  "L2 norm" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: added recently two new sections to this article, "Basic properties", and "Normability". For the reasons that follow, these sections do not belong to this article. By lazyness, I have reverted the article to the last version before this addition, and this resulted in reverting also edits (including by myself) to the other parts of the article. Mgkrupa restored my edits and the reverted sections. I'll remove these sections again for the following reasons.
Section "Normability" is not about the subject of this article, not even about normed vector spaces, it is about a property of topological vector space. It has nothing to do here.
Section "Basic properties" is not about basic properties of norms as suggested by its title. It starts by a nonsensical sentence implying the concept of a ball of given radius in a vector space that is not supposed to be a normed vector space. If this is fixed by supposing that the vector space is normed, most properties are not basic properties of norms, but properties of seminorms defined on a TVS or a normed vector space. Only properties 1, 3, and 4 are basic properties, but they are stated as properties of seminorms, without stating that they are also true for norms. All other properties are properties of seminorms on a topological vector space. This does not belong the first section after the definition. D.Lazard (talk) 08:39, 16 July 2020 (UTC)
thread_title:  Recently added sections 

message: In the Equivalence section, where is says "For instance, if p > r > 1", Shouldn't it actually say "p > r >= 1"?  — Preceding unsigned comment added by 2601:644:400:5FF0:5E0:73E:C912:D92B (talk) 21:37, 25 November 2020 (UTC)
replies: text: You are right, as the 1-norm is considered in the next sentences. I have fixed this. D.Lazard (talk) 08:40, 26 November 2020 (UTC)
thread_title:  r >= 1 ? 

message: In many articles when the field in question is ℝ or ℂ, it is written \mathbb{K}\in\{\R,\Complex\}. In this article it is 𝔽 or 𝔽. I'd like to prefer the first – and only upright. –Nomen4Omen (talk) 21:56, 13 December 2020 (UTC)
thread_title:  Notation 

message: Hi, the word "non-negative" (with a hyphen) is more common than nonnegative. For example see https://en.wikipedia.org/wiki/Sign_(mathematics)#non-negative_and_non-positive. Hooman Mallahzadeh (talk) 17:01, 8 March 2022 (UTC)
replies: text: I reverted your edit because both spellings are acceptable, and thus MOS:VAR applies. However, consistency is more important. Later, in the article, there are (in the same section) "non-negativity" and "nonnegativity". So this must be changed, and we must choose between the two spelling. I agree that "non-negative" is more common in Wikipedia. So, I agree to add an hyphen to all occurences (in the article) where it is lacking. D.Lazard (talk) 22:04, 8 March 2022 (UTC)
thread_title:  nonnegative or non-negative? 

message: An editor has identified a potential problem with the redirect :L² norm and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 May 4#L² norm until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  fgnievinski (talk) 22:03, 4 May 2022 (UTC)
thread_title:  "L² norm" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: An editor has identified a potential problem with the redirect :L2 norm and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 May 4#L2 norm until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  fgnievinski (talk) 22:04, 4 May 2022 (UTC)
thread_title:  "L2 norm" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: An editor has identified a potential problem with the redirect :Square norm and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 May 4#Square norm until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  fgnievinski (talk) 22:04, 4 May 2022 (UTC)
thread_title:  "Square norm" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: An editor has identified a potential problem with the redirect :Pseudonorm and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 May 11#Pseudonorm until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  1234qwer1234qwer4 20:35, 11 May 2022 (UTC)
thread_title:  "Pseudonorm" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: In the 'Euclidean Norm' section, the Euclidean norm is first denoted ||x||_2, then as ||x||. Is the subscript 2 important in the first instance? If so, why does it disappear? And if not, why include it in the first place? The article should either be consistent, or explain why there is a difference between the two notations. Lhommedacier (talk) 09:51, 8 August 2023 (UTC)
thread_title:  Subscript consistency  

message: We use  in
Given a vector space X over a subfield F of the  complex numbers \Complex, a norm on X is a real-valued function p : X \to \Reals with the following properties, ...
and in the section on -norms
Let p \geq 1 be a real number.
The p-norm (also called \ell^p-norm) of vector \mathbf{x} = (x_1, \ldots, x_n) is ...
I think that using  for both these roles is confusing and I would like to change the former.  (The latter is very much conventional use.)  Is there a letter other than  that is typically used in textbooks for a function on a vector space that is a norm? —Quantling (talk | contribs) 14:32, 6 September 2023 (UTC)
thread_title:  Overuse of the letter p 

message: The article claims that some people define a pseudonorm by weakening the identity
:\forall a\in\mathbb F~\forall v\in V~~p(av) = |a|p(v)
to an inequality:
:\forall a\in\mathbb F~\forall v\in V~~p(av)\le|a|p(v). 
However, the claim needs more substantiation—the setup described by the reference (Kurosh's Lectures in General Algebra, 1965, via Encyclopedia of Math) is different; Kurosh talks only about normed rings, where a,v belong to some common ring R. Does anyone have a better reference? Thatsme314 (talk) 22:17, 22 April 2024 (UTC)
thread_title:  Encylopedia of Math definition of pseudonorm