lflage/wiki-talks huggingface dataset:
Talk:Hankel matrix

message: does the material presented in the section Hankel transform correct? I can make a simple example to violate it! For example, take b1=1, b2=1, b3=2 and you will have detB=1 but detC=-1!  —Preceding unsigned comment added by 61.18.170.199 (talk) 09:46, 6 August 2009 (UTC)
replies: text: formula is now correctBPets (talk) 04:34, 1 September 2009 (UTC)
replies: text: Please improve the section on system identification... it currently doesn't begin to suggest how one might actually do this.--Witbrock (talk) 18:15, 2 May 2013 (UTC)
thread_title:  Hankel transform as presented in the text correct? 

message: Bhajan123 (contributions) (talk) has been including references to R. B. Pachori in several articles.  Bhajan123 may simply be promoting his or her own work.  I recommend removing such references. — Anita5192 (talk) 19:41, 31 July 2016 (UTC)
replies: text: They were removed sometime in the past. Also, user was blocked about a year ago. 67.198.37.16 (talk) 00:00, 15 January 2024 (UTC)
thread_title:  Reference to R. B. Pachori 

message: I can't make any sense of the statement "A  must satisfy, for all rows i and columns j, (A_{i,j})_{i,j \ge 1}. ". Is this perhaps a typo? Andylatto (talk) 17:50, 23 June 2021 (UTC)
replies: text: I removed this section. It was garbled, presumably copied from class notes. It was trying to define the Hankel operator, which was already defined in the previous section. 67.198.37.16 (talk) 00:27, 15 January 2024 (UTC)
thread_title:  Confusing statement 

message: I just removed the following, because it doesn't say anything useful:
:Given a Hankel operator H_\alpha: \ell^2\left(\mathbb{Z}^+ \cup\{0\}\right) \to \ell^2\left(\mathbb{Z}^+ \cup\{0\}\right) over the Hilbert space \ell^2(\mathbb Z), the space of square-integrable bilateral complex sequences, and given any u \in \ell^2(\mathbb Z), then
::\|u\|_{\ell^2(z)}^2 = \sum_{n=-\infty}^{\infty}\left| u_n \right|^2.
The display formula is merely the definition of the norm on that Hilbert space. That norm has nothing to do with the Hankel operator. Thus, it "doesn't say anything useful". Perhaps the intent was ... to say something more? Viewing the article history, this was added by User:Cyphra in May 2020, and there was never anything more than this. 67.198.37.16 (talk) 22:29, 25 January 2024 (UTC)
thread_title:  Remove empty statement
Talk:Central simple algebra

message: It would be very helpful if with the statement
"Given two central simple algebras A ~ M(n,S) and B ~ M(m,T) over the same field F, A and B are called similar (or Brauer equivalent) if their division rings S and T are isomorphic."
a) the notation "~" and "M(n,S)" and "M(m,T)" is explained, and
b) the reason for using these equivalences is also explained.
In an encyclopedia is it not good enough to merely write something that is mathematially correct. It must be understandable as well. 2601:200:C000:1A0:90E6:F29F:F511:B9ED (talk) 18:25, 8 June 2021 (UTC)
thread_title:  Suggested improvement
Talk:Simple ring

message: As far as I can tell, simple algebra and simple ring discuss the same concept; hence, the merger is in order. -- Taku (talk) 01:01, 10 January 2020 (UTC)
replies: text: Sorry, I meant to say except the section on universal algebra. The problem is that currently, despite the article title, the article simple ring is mostly about a simple algebra. I didn’t mean to say the two concepts are the same; I was referring to materials. I have gone ahead with the partial merger and renamed the simple algebra to simple universal algebra (since I doubt the primary meaning of a simple algebra is one in universal algebra). Simple algebra now redirects to simple ring. —- Taku (talk) 16:35, 28 April 2020 (UTC)
thread_title:  Merge from [[simple ring]] 

message: It's not true that any left ideal of a matrix ring $M_n(D)$ has the claimed form. The left ideals correspond to $D$-linear subspaces of $D^n$, where a $D$-linear subspace $L \subset D^n$ is associated to the ideal of $M_n(D)$ where each row has entries from $L$. Not all such subspaces are given by setting a subcollection of coordinates to zero, even when $D$ is a field.  — Preceding unsigned comment added by 2601:246:100:2B00:5430:9CE2:C024:D606 (talk) 18:35, 11 January 2022 (UTC)
replies: text: A simple counterexample to the claim is the ideal I =\{[v|v|\dotsb|v] : v \in D^n \} . This is clearly an ideal that doesn't fit the article's description. --Svennik (talk) 18:45, 7 February 2022 (UTC)

text: Hold on. It's incredible that this mistake has existed since circa 2005. Just look at the history of this article! Does anybody actually check this stuff? --Svennik (talk) 18:52, 7 February 2022 (UTC)

text: The proof of Wedderburn-Artin on this page was completely bogus, for the reason Svennik explained.  I deleted it and added a bunch of new material on simple rings.  There is a proof of Wedderburn-Artin on the page Wedderburn-Artin theorem, and I think that's the right place for this proof. John Baez (talk) 19:15, 12 June 2023 (UTC)
thread_title:  Ideals in matrix rings
Talk:Matrix ring

message: Probably a significant amount of matrix rings over division rings should just be covered under the Artin-Wedderburn theorem or semisimple ring or so.
Identification of rings as matrix rings is relatively interesting.  For instance, if M_n(R) =~ M_m(S), must m=n or R=~S?  A good reference for interesting items to add along these lines is Lam's Modules and Rings, the first chapter in the Morita equivalence section.  I think this might be the main hope.
One could certainly add some trivial Morita corollaries to the properties list, but that only makes the article longer, not less stubby.  One could link to the Jacobson density theorem which says rings with faithful primitive modules (like Matrix rings over division rings) are very nearly matrix rings over division rings. 
One could link to Brauer group or Central simple algebra where matrix rings play the role of the identity element or trivial example, but again this is mostly an Artinian simple ring thing. JackSchmidt 23:34, 3 December 2007 (UTC)
thread_title: How to unstubbify?

message: If n≥2, then Mn(R) is noncommutative and has lots of zero divisors, nilpotents, and idempotents. GeoffreyT2000 (talk) 15:00, 28 February 2015 (UTC)
thread_title:  Properties 

message: In the Banach algebra example, some of the statements about infinite matrices look false to me.  Does anyone know what they were intended to be?  Is there a reference? Ebony Jackson (talk) 02:46, 26 December 2020 (UTC)
thread_title:  Banach algebra
Talk:Reduced ring

message: Thank you Darij for fixing my mistake. However, the criterion
* every element a\in A satisfying a^2=0 is zero itself
is also wrong: the ring Z/6Z satisfies this criterion but is not reduced. I have fixed this. Ninte (talk) 11:09, 20 October 2010 (UTC)

message: Suppose that a^n=0. If n is even, divide it by 2. If n is odd, add 1 to it and divide by 2. Repeat this process until n=1, and then a=0. GeoffreyT2000 (talk) 01:56, 2 May 2015 (UTC)
thread_title:  Proof
Talk:Noetherian module

message: I added a little bit about the history of the definition LkNsngth (talk) 06:05, 18 June 2008 (UTC)
replies: text: Aren't  2\mathbb{Z},3\mathbb{Z} both maximal elements of th set \{ 2\mathbb{Z},3\mathbb{Z} \}? (Maximal in the sense there is no other element properly containing it.) -- Taku (talk) 04:32, 11 November 2015 (UTC)

text: @Ajkirk Taku's comment is right. It looks a bit like you are thinking about a maximum element of a set rather than maximal elements. Could this be the case? Rschwieb (talk) 14:35, 11 November 2015 (UTC)
Talk:Simple algebra (universal algebra)

message: "The second condition in the definition precludes the following situation: consider the algebra
    \{ \begin{bmatrix} 0 & \alpha \\ 0 & 0 \\ \end{bmatrix}\, | \, \alpha \in \mathbb{C} \}
with the usual matrix operations"
in my opinion, this is NOT algebra, because there is not "1". And the algebra HAS (in respect to this wikipedia page: http://en.wikipedia.org/wiki/Algebra_%28ring_theory%29) to be a ring with unit! I hope that my terrible english is comprehensible at least--80.180.27.186 (talk) 08:32, 11 September 2009 (UTC)
Talk:DHL International Aviation ME

message: Is the fleet in this article based on latest data?--BR141 (talk) 18:12, 21 August 2014 (UTC)
thread_title:  Fleet 
Talk:Perfect group

message: the realm of group theory ? 'tf is that ?! just say  "in group theory"  —Preceding unsigned comment added by 188.26.49.101 (talk) 01:41, 21 April 2010 (UTC)
replies: text: "In group theory" is definitely the prominent phrase in most Wikipedia mathematics article. However, every author has a different style, and perhaps those involved in writing the opening of this article felt that "the realm of group theory" fits better in the sentence. That said, it is irrelevant to the article as a whole; if you wish to change it, you are most welcome to do so and I do not think anyone will object. PST 02:12, 21 April 2010 (UTC)

message: Perhaps I am just being silly, but I feel that the phrase
"More generally, any non-abelian simple group is perfect since the commutator subgroup is a normal subgroup with abelian quotient."
is perhaps unnecessarily complicated as it requires the reader to piece together a few implications. More precisely, the reader must realize that since the group is simple, it has no non-trivial normal subgroups implying that the commutator is either  G   or  \{e\} . Now if [G,G] = \{e\} then G/[G,G]=G is abelian, but this is not possible, hence  [G,G] = G  and the group is perfect. This could be written much simpler by just saying that a non-abelian simple group only has quotients  G   or  \{e\}, one of which is trivial and the other of which is abelian. However, if someone objects I won't bother to change it. Kreizhn (talk) 20:58, 12 March 2013 (UTC)
thread_title:  Unnecessarily complicated wording?
Talk:Cassiopeia (1996 film)

message: I've noticed that a lot of the things in this article are made to prove that Toy Story wasn't "entirely computer generated" Toy Story absolutely was. Please fix this article. WiinterU (talk) 11:25, 19 March 2023 (UTC)
thread_title:  Get rid of biased material
Talk:ADE classification

message: I believe that something like the following is true:
:The irreducible representations of the binary polyhedral groups correspond to the nodes of the associated ADE Dynkin diagram,
:and the dimension of the representation are the labels discussed in Proctor.
I’m pretty sure these labels are some form of dimension of a representation, as indicated in (Proctor 1993), but he doesn’t elaborate, and I can’t find references that do, so for now I’ll leave this on the talk page.
Any (referenced) elaboration would be much appreciated!
:—Nils von Barth (nbarth) (talk) 23:22, 26 April 2010 (UTC)
thread_title:  McKay correspondence 

message: For some reason, Buckyball surface redirects here.  The lead should explain why. 2606:A000:4C0C:E200:5CA2:EAF0:ADD:D9B (talk) 19:21, 10 September 2016 (UTC)
thread_title:   Buckyball surface? 
Talk:Syntactic monoid

message: The link at the beggining of the article "recognizable language" doesn't make sens. It liinks to "recursive enumerable language" and not to recognizability by finite monoïd. I think one has to create a new page to explain this definition, or may be to add it to the monoïd page.  — Preceding unsigned comment added by Arthur MILCHIOR (talk • contribs) 20:48, 22 October 2012 (UTC)
replies: text: No, it is right.  The case of a finite monoid is different, there you are looking at a regular language.  Deltahedron (talk) 21:49, 22 October 2012 (UTC)
thread_title: Recognizable language
Talk:Complemented lattice

message: I wonder if the obvious involution in a uniquely complemented lattice is an orthocomplementation. --Hans Adler (talk) 15:11, 7 February 2008 (UTC)
thread_title:  Uniquely complemented but not orthocomplemented? 

message: "In distributive lattices, complements are unique." Add if they exist
Not all distributive lattices have a complement for every element. And not all complemented lattices are distributive. So the next sentence should make it clear:
"Every complemented distributive lattice ..." is talking about a subset of complemented lattices and a subset of distributive lattices. This map shows it clearly.
AntC2 (talk) 00:34, 5 January 2020 (UTC)
thread_title:  Complemented Distributed Lattice
Talk:Complete group

message: If someone has time, both Rotman and Robinson group theory texts have a nice little discussion of complete groups and the automorphism tower problem.  It would be good to mention the tower problem and add an explicit reference or two. JackSchmidt 01:43, 30 August 2007 (UTC)

message: Do there exist groups G that are isomorphic to their own automorphism groups but such that the canonical homomorphism from G to Aut(G) is injective but not surjective, or surjective but not injective? GeoffreyT2000 (talk) 23:24, 8 May 2015 (UTC)
thread_title:  Injective and surjective
Talk:Schreier refinement theorem

message: I think the term "normal series" is misleading.
while "normal series" is correctly linked to an article discussing subnormal AND normal series,
that exact article says that subnormal series is a weaker sense of normal series
by giving the term normal series the property that each subgroup in the series is also
normal in the first group.  — Preceding unsigned comment added by Mangoish (talk • contribs) 18:47, 9 November 2012 (UTC)
Category talk:Fiction about incest

message: I don't know how to edit either, so I'll let someone else do it (hopefully!)  The 1991 movie Close My Eyes  with Alan Rickman, Clive Owen & Saskia Reeves.  —Preceding unsigned comment added by 208.141.110.251 (talk) 07:14, 13 March 2008 (UTC)
replies: text: Done. --zenohockey (talk) 18:33, 13 March 2008 (UTC)
thread_title:  Another Movie to add 

message: Creepy.
66.87.2.142 (talk) 06:45, 7 November 2012 (UTC)
thread_title:  This is a really creepy category
Talk:Ideal quotient

message: If memory serves, the equality Z(I : J) = \text{cl}(Z(I) \backslash Z(J)) only holds when I is reduced. --Linus44 (talk) 15:24, 16 July 2013 (UTC)
replies: text: @128.210.4.87 Defining J^\infty = \sum_{i=1}^\infty J^i was surely wrong. Maybe it would be good to also mention J^\infty = \bigcap_{i=1}^\infty J^i ? At least, I have seen this in other contexts, and I assume that the order reversing property of the ideal quotient in the right entry agrees with this. Rschwieb (talk) 21:49, 3 November 2015 (UTC)

message: Presumably this article assumes rings to have multiplicative identities? (otherwise several of the listed properties would not hold) - If so, this should be mentioned in the introduction. Joel Brennan (talk) 17:28, 28 March 2022 (UTC)
thread_title:  Ring identity
Talk:Bioartificial liver device

message: Wildly inconsistent. Several different methods of performing it. Article currently references things so I was not sure how to edit, but did fix a key aspect. Author may have misinterpreted the articles.  —Preceding unsigned comment added by 130.113.128.11 (talk) 21:01, 16 November 2009 (UTC)
thread_title: Function
Talk:Archimedean field

message: The Archimedean property article indicates this article as the main one, yet is much more detailed and entirely subsumes this "main" article.  Is there any reason to retain this stub, as opposed to simply making it a redirect to Archimedean property?  --Vaughan Pratt (talk) 03:22, 30 January 2009 (UTC)
thread_title: Merge with [[Archimedean property]]?
Talk:Projectionless C*-algebra

message: What is the definition of projection used here?  I would guess it refers to idempotent elements, but I'm not entirely sure.  69.234.16.148 (talk) 23:12, 12 August 2008 (UTC)
replies: text: For C*-algebras, projections are self-adjoint idempotents. For concrete C*-algebras, they correspond to orthogonal projections, which is probably where the name comes from. Minimalrho (talk) 02:54, 1 March 2013 (UTC)
replies: text: Yes, the article should be renamed "Projectionless C*-algebra" and include some non-trivial examples, like the first one by Blackadar or the reduced group C*-algebra of a free group. Mct mht (talk) 09:28, 1 March 2013 (UTC)
thread_title: Untitled
Talk:Form 10-K

message: FILING DEADLINES I don't think anyone cares about the history of the filing deadlines. This section is confusing and should be streamlined to more simply explain what the deadlines are. 208.90.12.47 (talk) 14:40, 19 April 2017 (UTC)

message: https://www.instagram.com/chavadiyabachu2023?igsh=MTEzdnFjNWducHo2 49.34.175.157 (talk) 16:30, 14 May 2024 (UTC)
thread_title:  https://www.investopedia.com/dow-jones-today-05142024-8648016#toc-2024-05-14t132730838z 

message: https://www.instagram.com/chavadiyabachu2023?igsh=MTEzdnFjNWducHo2 49.34.175.157 (talk) 16:30, 14 May 2024 (UTC)
thread_title:  10m 

message: https://www.instagram.com/chavadiyabachu2023?igsh=MTEzdnFjNWducHo2 49.34.175.157 (talk) 16:31, 14 May 2024 (UTC)
thread_title:  https://www.instagram.com/chavadiyabachu2023?igsh=MTEzdnFjNWducHo2
File talk:Asukka13.jpg

message: Is this an original artwork or a screen capture from the anime?  If it's the latter, it needs to be tagged with the proper template and given a fair use justification or it'll get removed. Willbyr (talk | contribs) 20:32, 16 March 2007 (UTC)

message: Purpose and Resolution edited per FU guidelines. Willbyr (talk | contribs) 15:27, 17 July 2007 (UTC)
thread_title:  Fair use
Talk:Correspondence theorem

message: I generally don't care what a page is called but in this case it seems that "Lattice theorem" is a rather uncommon name for this. Besides Scott's textbook, which indeed does call it this way, is there anything else calling it this? Pretty much every other book I've looked in calls it either "Correspondence theorem" or 4th isomorphism... 86.127.138.67 (talk) 02:49, 17 April 2015 (UTC)
thread_title:  Title
Talk:Cyclic homology

message: This page should discuss results from https://faculty.math.illinois.edu/K-theory/0046/root.pdf  — Preceding unsigned comment added by 128.138.65.175 (talk) 23:48, 7 September 2017 (UTC)
thread_title:  Hodge Structures and Cyclic Homology
Talk:Mixed layer

message: I'm preparing an article on convective mixing in the atmospheric boundary layer (ABL) as part of an UCLA class project (The Atmospheric Boundary Layer ). I already gathered some references in my sandbox. Any feedbacks would be really appreciated.  --Lethepku (talk) 22:48, 2 May 2014 (UTC)
thread_title: Related Articles

message: The article talks about the ocean mixed layer in some places and oceanic in others.  Although both are used, shouldn't Wikipedia pick one and stick to it?  Vaughan Pratt (talk) 00:24, 15 November 2014 (UTC)
thread_title: Ocean or oceanic
Talk:Frobenius algebra

message: I expanded the article a bit and gave a good reference for history and algebraic study of Frobenius algebras.  In particular, everything up to the categorical stuff is easily found in Lam (which has several sections on Frobenius algebras), and everything after is unsourced, but I remember some Baez article about this.
I did not actually include the duality theory which plays a prominent role in the study of Quasi-Frobenius rings and Iwanaga-Gorenstein rings.  In particular, I did not include the classical contributions of Nakayama (because he has no wiki bio!) on the Nakayama permutation, the relations amongst the simple modules, and socle/head duality.  Nor did I include Nakayama's term for these algebras, Frobeniusean, since he is the only one who used it more than once.  Similarly, symmetric algebras received almost no special treatment, even though they are a fundamentally important special case.  The generalizations to Frobenius rings, Quasi-Frobenius rings, and self-injective rings are not included here, but perhaps this would be a good place if quasi-frobenius does not get its own article.  Lam would provide a good reference for the intuitive differences between these notions, but for generalizations of QF, one needs to look elsewhere (Faith's Rings and Things for instance has quite a few such generalizations). JackSchmidt (talk) 09:19, 23 November 2007 (UTC)
replies: text: Lam also acts as a source for the TQFT remarks, but has nothing on the categorical definition.  I included a few other remarks too. JackSchmidt (talk) 09:55, 23 November 2007 (UTC)
thread_title: Expanded

message: Is it correct that there's no requirement on the characteristic of the field k in the definition of Frobenius algebras?
HSNie 14:56, 31 May 2013 (UTC)
thread_title:  Characeristic of the field?

message: Some topics need expansion:
* Need defintion of a dagger frobenius algebra. This algebra is used to define the basis in a dagger compact category.
* The dagger frobenius algebras somehow convey classical information, because they can evade the no-colning/no-deleting theorems.  This should be clarified.
* Need to cleanup the statements about TQFT, so, e.g. Atiyah says any TQFT is just a functor between nCob and FDHilb  both of which are dagger compact. This article never goes there.  so ???
User:Linas (talk) 05:09, 28 November 2013 (UTC)
thread_title: TODO list

message: Naively, trace-class operator algebras would be seem to fit the profile; why the restriction to fininte? User:Linas (talk) 06:28, 28 November 2013 (UTC)
thread_title:  why finite-dimensional? 

message: Could someone please expand upon where Frobenius algebra would be covered in a typical mathematics curriculum?  — Preceding unsigned comment added by 67.52.192.26 (talk) 15:13, 20 June 2014 (UTC)
thread_title:  Place within mathematics curriculum
Talk:Section (mathematics)

message: This article needs to move to section (group theory), so that section (mathematics) can be made into a dab. Geometry guy 16:38, 22 May 2007 (UTC)
replies: text: I've done the move, and made this a dab. It wasn't worth messing around with the edit histories, as they are very short, and it is not clear which history really belongs with which page. I've generally reorganised the various section pages and fixed links. Geometry guy 17:50, 23 May 2007 (UTC)
Talk:Pro-p group

message: In what sense is \mathbb Z_p the canonical example?  Does it satisfy a universal mapping property? --345Kai (talk) 16:53, 26 June 2017 (UTC)
replies: text: I think that in this context it's meant only to indicate that it is the simplest (non-finite) example. On the other hand, I guess it also has an important role in the general theory as it is the "pro-p cyclic group" : in a pro-p group every element of infinite order topologically generates a copy of \mathbb Z_p. jraimbau (talk) 14:08, 27 June 2017 (UTC)
thread_title:  canonical example?
Talk:Metabelian group

message: Hi, I'm wondering if residually abelian would be the same or related to metabelian. For all I know, residually abelian might actually imply abelian. Thanks, Richard Peterson198.189.194.129 (talk) 23:25, 14 March 2012 (UTC)
replies: text: Residually abelian is the same as abelian. --Zundark (talk) 09:14, 15 March 2012 (UTC)
replies: text: thanks would you care to say why?198.189.194.129 (talk) 00:28, 16 March 2012 (UTC)
replies: text: If you look at the definition of residually X, in the case where X is "abelian" it essentially says "every non-identity element lies outside the derived subgroup" - i.e., the derived subgroup is trivial. --Zundark (talk) 12:46, 16 March 2012 (UTC)
thread_title: Metabelian groups and "residually abelian" groups