Talk:Classical group

message: I strongly oppose merging "Matrix group" and "Classical Lie group".  They are very different topics.  A matrix group is any group of matrices.  It may be finite, it may have coefficients in a finite field, it may be a topologically discrete subgroup of a classical Lie group, etc.  A classical Lie group is a manifold with group structure; this gives it very particular properties.  There are different questions and results that belong to the two topics.  Zaslav 20:49, 26 March 2007 (UTC)
replies: text: I think what is meant here is to merge the section on classical groups from the article "matrix groups" into this article, where it would fit better. Perhaps, the title would have to be changed to "Classical group". This would allow us to concentrate on the general properties of matrix (i.e. linear) groups in the Matrix group article, as opposed to descriptions of classical groups, as is presently the case. Arcfrk 22:08, 4 April 2007 (UTC)

message: There is no way this article is class B, so I gave it a "Start" rating. The subject has inspired much classical research, many books, and is the backbone in any course beyond "abstract group theory". It deserves a much more inspired article.
In today's terminology there are the complex classical groups, the real classical groups and the compact classical groups. Variants exist; the connoisseur might add the exceptional groups, others relax the determinant = 1 condition to determinant = +/-1, yet others include also  and some quaternion groups (. The groups  and  (coming from indefinite Hermitean forms on , see below) are missing all-together in the article.
The unifying framework is bilinear forms on  and , sesquilinear forms on  and . These forms can be symmetric or antisymmetric (in the bilinear case), Hermitean or anti-Hermitean (in the sesquilinear case). 
On the other hand, the section Classical groups over general fields or rings is a completely unnecessary extension of the subject. It is far from the classical considerations.
An introductory exposition of these forms and their signatures, could explain all terminology and some connections between the groups. A beefier explanation of 'compact real form is also called for. 
Most (all actually, and much more) of what I propose could be extracted from §3.1 in Wulf Rossmann's "Lie Groups, an Introduction through Linear Groups". YohanN7 (talk) 13:38, 2 January 2014 (UTC)
thread_title:  Not B-class 

message: A while ago, I changed the article rating from B-class to start-class (motivated above). Someone now changed this to C-class with the motivation that "article ratings aren't arbitrary". Right, they aren't—at least they shouldn't be. This article is very incomplete in coverage, covers stuff not relevant to the subject, and contains several errors. There are plenty of articles that are complete, correct, and good reading, but will never get a C-class rating because the subject is narrow and will never motivate more than one page of text. (I disagree with this rating policy b t w.)
This article is one page (at least upon removal of irrelevant stuff) on a fully developed huge classical topic that is extremely useful in modern applications. (You can take it to the extreme point that modern theoretical physics is the theory of particular symmetries without exaggerating very much. These symmetries are often described by classical groups.) With this in mind, the article is, in my opinion, smack dab start-class, even a pretty good start-class article, but it is not C-class. I will not change the rating back unless others agree with me, and I can live with this as an unusually poor C-class article. 
Of course, I'm not blaming the article's authors. They, at least, wrote it, giving it a solid start. I'm merely complaining. I wish I had the time to develop the article, but I don't. YohanN7 (talk) 14:43, 29 April 2014 (UTC)
thread_title:  Not C-class 

message: I rewrote the article from scratch but retained the section Classical groups over general fields or algebras. I think it should go elsewhere (or be scrapped) because it isn't in the spirit of classical groups. YohanN7 (talk) 18:33, 11 July 2014 (UTC)
replies: text: Does  like serif \mathrm{\mathrm{T}} for transpose due to aversion to any use of sans-serif in math notation? Incnis Mrsi (talk) 07:58, 18 August 2019 (UTC)
replies: text:  Does Incnis Mrsi make unnecessarily aggressive, personalized comments because they are opposed to any forms of polite engagement? --JBL (talk) 23:47, 23 August 2019 (UTC)
thread_title:  New version 

message: Near the end of the section titled Quaternionic case this passage appears:
"The determinant of a quaternionic matrix is defined in this representation as being the ordinary complex determinant of its representative matrix. The non-commutative nature of quaternionic multiplication would, in the quaternionic representation of matrices, be ambiguous.'"
But it is not the "non-commutative nature of quaternionic multiplication" that would be ambiguous; it is the definition of the determinant of a quaternionic matrix that would be ambiguous. 2601:200:C000:1A0:1976:AC3F:FBA4:37D4 (talk) 17:17, 4 October 2021 (UTC)
thread_title:  Unclear statement