# Should questions on (matrices) and (matrix-equations) be also tagged as (linear-algebra)?

Recently the following text was added to linear algebra tag-excerpt:

For questions specifically concerning matrices, use the (matrices) tag. For questions specifically concerning matrix equations, use the (matrix-equations) tag.

The same user who added this text started removing from questions tagged and . Today another user made rollbacks to many of these edits.

I think that to avoid editing/retagging wars it would be better to know where the community stands on this and whether other users agree with the recent change to the tag-excerpt.

• We should probably ask the proposer and the ones who approved the proposal. In any event, I'm not seeing the logic in removing linear-algebra from matrix-related questions. May 17 '13 at 8:27
• I've pinged him (=the proposer) on one of the questions he edited, I hope he will come to meta. May 17 '13 at 8:30
• Hehe, I was just typing up a very similar question. I'll ditch mine.
– mrf
May 17 '13 at 8:32
• Dear Martin Sleziak: Thank you for asking this question here, which is exactly what I want to know.
– 23rd
May 17 '13 at 8:37
• Do we really need 2 matrix tags? I would burninate the matrix equations tag. And when a matrix question has no relation to linear algebra (which I suspect doesn't happen that often) the linear algebra tag should be removed, but else it shouldn't May 17 '13 at 9:17
• I accepted it since it makes some sensible tag suggestions. It doesn't say not to tag them linear-algebra also. (I was unaware of the tag removals you noted.) May 17 '13 at 12:29
• @doraemonpaul I fail to see why this should be tagged as feature-request, so I have removed the tag you have added. May 19 '13 at 5:07
• @Martin Sleziak: read carefully on my answer, you will understand why I add the feature-request tag. May 19 '13 at 9:03
• @doraemonpaul Do you mean the last paragraph starting So MSE is better to modify the system as "main page holds zones, zones hold tags" concept? If you want to propose some changes to tagging system at SE, you should post it as a separate feature-request; either here or at meta.SO. Having a question tagged feature-request, which contains no feature request at all, only something akin to a feature request is buried in one of the several answers, seems strange to me. May 19 '13 at 9:24
• Now on meta after "matrices": an inappropriate retagging and a rollback to that inappropriate retag. May 19 '13 at 12:58
• I'd say leave linear algebra and matrices, take out matrix equations.
– Alexander Gruber Mod
May 20 '13 at 0:30

Do we really need 2 matrix tags? I would burninate the matrix equations tag. And when a matrix question has no relation to linear algebra (which I suspect doesn't happen that often) the linear algebra tag should be removed, but else it shouldn't.

• Turned the comment in an answer so we can see what the community thinks May 17 '13 at 9:51
• Well, if people have been asking a lot of questions on matrix polynomials, or nonlinear matrix equations, or even things like the Riccati or Sylvester equations, the the existence of matrix-equations is justified. May 17 '13 at 9:52
• @J.M. My hope that those "Solve $Ax=b$ questions" aren't tagged as matrix equations is very limited. And as far as I can see there are no questions which seems to be specific to matrix equations May 17 '13 at 9:59
• Oh, certainly $\mathbf A\mathbf x=\mathbf b$ is outside the scope; the definition I am accustomed to is that your unknown is a matrix, and vectors are usually excluded from this. You are right that someone who doesn't know better might mistag, tho. But I do recall seeing not a few Sylvester-related questions and at least some on matrix polynomials. May 17 '13 at 10:02
• .. and some on matrix-series (exponential/logarithm of matrices) (however I don't recall whether they were stated as questions on matrix-equations ) May 17 '13 at 12:33
• @Dominic Michaelis, can you tell me the borderlines that when do the questions related to matrix and linear algebra, when do the questions related to matrix but not related to linear algebra? May 17 '13 at 12:41
• @Gottfried Helms, it is better to classify them as matrix functions, which also is one of the tag I will consider to create. May 17 '13 at 12:45
• @doraemonpaul, we were expecting you to explain why you did those tag removals... May 17 '13 at 13:16
• @doraemonpaul If both apply you can still use both (if your question really needs more than 5 complete distinct tags it may be a sign it is to broad). And I please you not to create a matrix function tag. Matrix functions and regular functions are absolutely the same. A function is the special case of an arrow, having a an object als codomain and one as domain no big thing. Making so many nearly the same tags helps absolutly nothing May 17 '13 at 13:17

In general I don't see much harm in leaving on questions that actually concern linear algebra. When matrices themselves are the central objects of study (as opposed to the vectors and vector spaces on which they act) the tag seems misplaced to me.

The issue here seems to be that gets used for things that are not really "matrix equations", but usual linear algebra. Part of this behaviour can IMO be traced to the fact that it's not immediately obvious what qualifies as a "matrix equation".

For this reason, I propose to rename this tag to instead. This tag should be used to govern things like exponentiation of matrices, Sylvester polynomials, Cayley-Hamilton, etc. It could be used in conjunction with the tag but I think not with the tag.

A bonus of picking is that it contains the word "algebra", and I imagine people are less likely to include two different types of "algebra" tags on their questions.

The only thing I did not address was . I have no clear idea what to do with it. Perhaps its tag wiki could suggest using or when only one of those is applicable.

• (+1) for the "bonus picking". Very nice contemplation... May 17 '13 at 12:42
• The downside of (matrix-algebra) is that this word refers to the algebra $M_{n \times n}(R)$ of $n \times n$-matrices over a ring $R$. May 17 '13 at 13:00
• @Martin It's reminiscent of the ambiguity of the boolean-algebra tag, which can also refer to either Boolean algebras or the field Boolean algebra. I suppose the fine distinction between matrix-algebra and matrix-algebras is not something that can be easily conveyed. I'd be willing to try, though. Proper tag wikis and excerpts could go a long way. May 17 '13 at 13:30
• I certainly agree with the first part of your post. I am not so sure whether matrix-algebra is going to be useful. So I have neither upvoted, nor downvoted - and I will wait to see what other users say. May 19 '13 at 5:24
• You wrote: When matrices themselves are the central objects of study ... the (linear-algebra) tag seems misplaced to me. I'll just add to that that if an answer is given which uses linear algebra in some way (for example, if we use properties of the linear maps corresponding to those matrices), the (linear-algebra) tag seems fine to me. See the discussion older here: Retagging after an answer is given. May 20 '13 at 6:59

Currently, I don't see any merit in using the "matrices" tag. Tags in MSE are not hierarchical and what should be regarded as "matrices" questions is unclear. Unless every "matrices" question is also tagged "linear-algebra", when we perform a search in the "linear-algebra" category, it is easy to miss the "matrices" questions. I have run into this trouble many times.

A deeper question is: shall we enforce a hierarichical system of tags? That is, whenever we encounter a "matrices" (or "determinant") question, shall we always also manually add a "linear-algebra" tag? If so, I don't mind keeping the "matrices" tag, even if it is not useful or descriptive.

That said, I think "matrix-equations" (and perhaps also "special-matrices") can be useful, provided that there are not too few questions of this kind. However, removing the "linear-algebra" in "matrix-equations" questions is not a good practice, I believe.

• You could simply search for matrices questions as well. The matrices tag is more informative than just plainly the linear-algebra tag; some people may not be interested in all of lin.alg., but only in matrices. Hierarchical tags are not the way to go -- only five tags are permitted per question. I disagree with matrices being "not useful or descriptive" and also with "removing the linear-algebra in matrix-equations is not good practice". May 18 '13 at 8:44
• @Lord_Farin "You could simply search for matrices questions as well" ... well, if the "matrices" tag is removed, I don't have to perform two searches in the first place. Deep hierarchy is certainly a problem. However, if we maintain a relatively flat hierarchy (say, there's only one level below "linear-algebra"), it may be more convenient for users. Currently, if you are not aware that a question may be tagged "matrices/eigenvalues/eigenvectors/determinant/etc.", it is rather difficult to search for them. I don't know your habit, but to me, this is a very real problem. May 18 '13 at 11:12
• @Lord, I suppose matrix-equations does straddle the boundary of matrix analysis and linear algebra, but I am curious as to why you disagree with the removal of linear-algebra not being good practice. May 18 '13 at 13:22
• I believe to have addressed this in the first paragraph of my answer. IMO not everything concerning matrices is linear algebra. A case-by-case analysis has to be made. I didn't want to imply that it is unconditionally good practice either. May 18 '13 at 13:24

In fact I want to make some major tidy-up of some tags.

Because I discover that many MSE users are having some problem habitats that like to tag their questions without careful considerations, they like either tag their questions with ''wide scope tags'' only or tag their questions with both ''wide scope tags'' and ''narrow scope tags'' , causing the ''wide scope tags'' often have too many questions but the ''narrow scope tags'' often have too few questions, reduce the efficiency of tag-using.

Typical examples are the tags of linear-algebra series, the tag has nearly $$10000$$ questions, the tag has nearly $$5000$$ questions, but for example the tag and the tag have only less than $$100$$ questions. The situation of the tags of linear-algebra series is alarming, as these will bring some large problems. For example the advanced-level questions such as about matrix functions and matrix equations will often fall into the oceans of ''wide scope tags'' such as the tag and often difficult to search them.

The tagging management system in MSE is so poor. The tagging rules in MSE is too generous. First, there are no punishment rules about inappropriate tagging behaviours. Second, as most MSE users often very busy on answering many questions to raising level to eventually become "top-level users" (reputations $$>20000$$ or even in multiples of $$10^5$$), or they are often afraid retagging will make OP unsatisfied or bump-up the questions and may make other users unsatisfied, therefore very less users take actions of both minor retagging or major retagging, with is often condisered as noxious by most MSE users.

So I decided to make some major retagging.

By recognizing some properties:

matrix-equations $$\subseteq$$ matrices $$\approx\subseteq$$ linear-algebra

matrix-functions $$\subseteq$$ matrices $$\approx\subseteq$$ linear-algebra

So my first operation is to create a tag, searching the questions about matrix equations and add the tag but removing the tag and the tag on them to bypass the horrible usages of the tag and the tag. For other matrix questions, keep the tag but removing the tag on them to bypass the horrible usage of the tag.

The result is quite well. I found more than $$100$$ known questions about matrix equations.

However, my operation makes some MSE users unsatisfied. Jared made an application of the tag merge into the tag (https://math.stackexchange.com/tags/synonyms). Landscape made rollbacks on most of the questions tagged (https://math.stackexchange.com/users/46120/landscape?tab=activity&sort=revisions). They both try to against my operation.

I don't understand why there are so many people like either tag their questions with ''wide scope tags'' only or tag their questions with both ''wide scope tags'' and ''narrow scope tags''. They should not be a good practice of categorization. Good categorization practice should be "categorize from specific to general" . Applying on our tagging system, the good tagging practice should be using the tags that are as specific as possible. ''wide scope tags'' should not use without careful considerations, unless you find that no ''narrow scope tags'' fits for your questions, otherwise many tags should require to use on each question.

Moreover, most mathematical branch names, e.g. algebra, linear algebra, calculus, etc. are no longer suitable to use as tag names, as they are too general to have too many questions belong to. They are better to upgrade as zone names.

So MSE is better to modify the system as "main page holds zones, zones hold tags" concept (i.e. the categorization system like http://answers.yahoo.com), to face growing numbers of questions. A few years ago the tag has been blacklisted (The use of the [algebra] tag). I think we should consider doing a similar thing on e.g. tag and tag.

• Apparently you misunderstand the reason for the blacklist of algebra. The reason is that it was ambiguous, that it could refer to either of what is now tagged abstract-algebra or algebra-precalculus, thus resulting in a most peculiar mix of questions. May 19 '13 at 3:11
• I do not think that having wide-scope tags is a bad thing. I believe they are useful when searching and when choosing the tags to follow. For example, if I am interested in general-topology, it is easier to me to favorite this one tag, than having to favorite also connectedness, compactness, (sequential-spaces), (hausdorff-spaces), (tychonoff-space) etc. (Of course, we do not have the last three tags, it is just a hypothetical example.) May 19 '13 at 5:21
• Perhaps I should also say that I appreciate that you care about correct tagging of questions. (There are many users who are too lazy to search for correct tags.) But large retaggings should not be done before some foregoing discussion. May 19 '13 at 9:25
• You're alone in this, as far as I can tell. While, as you noted, some users disagree with you. Maybe it is time for you to consider, just one second, that you might be wrong. May 19 '13 at 12:46
• One example: claiming that the latter is not "linear algebra" and only "matrix-equations" yields your answer, which tells nothing of interest regarding the equation $CA=C$. Just like your ignoring of diagonalization in that question. Try to think some more about that and hopefully you'll stop your inaccurate crusade, based on a peculiar understanding of linear algebra. May 19 '13 at 12:50
• At first I don't like to see when someone retags hundred of old questions because they will actually make questions which a really activate disappear to fast. I think you mix up the job of the tags with the job of the title of the question. Tags should be wide scope as it should give a rough topic of the question but not more. And punishing for wrong tagging is absolutely ridicolous. May 19 '13 at 15:54
• @Dominic Michaelis, I am really questioned about the real meaning of tagging you treated. Tagging act as an important role of categorizing questions in MSE, why you just treat it for example as only the slogan of attracting audiences, rather than to appreciate the essences of it? Anyway, nowadays, quite a lot of tags becomes like mass graves due to the poor management of the usage of tags, their evil consequence will only eventually return to us! May 19 '13 at 16:48
• Do you sometimes read what you write? Evil consequences of tagging something wrong? Maybe I just want to see the world burn. If we make categories of 20 member or less (Which will be a consequence if you split up every main tag into those ridicolus specialised sub tags, it is the same as just making no tags at all. This site is much to big and generates a lot of to many new question for such an exact specification May 19 '13 at 18:38
• Dear doraemonpaul, I was noticed when Martin Sleziak created this post and I followed this post since then. I didn't reply only because my English is not so good that I was afraid if I could express my opinion accurately. For a similar reason, when I was seeing your retaggings, I finally gave up my original thought to report this phenomenon to moderators, because I didn't know how to explain my attitude towards your retaggings and/or how to persuade them to agree with me. However, at the same time, I was incidentally in a bad mood and I couldn't understand your retagging behavior at all.
– 23rd
May 20 '13 at 4:50
• I couldn't understand because in om opinion, for most of the posts you retaged, "linear-algebra" and/or "matrices" best suit them and I didn't see any reason why you deleted (one of) them and added your tag "matrix-equations". I especially couldn't understand why you retagged so many old posts. Influenced by my bad mood at that time, I overacted to this by a crazy decision: rollback them. I have been calm down for a long while; I should apologize to you for my stupid behavior. I am glad to see my stupid behavior has some positive consequence: it leaded to the creation of this post.
– 23rd
May 20 '13 at 5:04
• I have read the question and almost all of the answers and comments here. I think my opinion has been expressed by others already, such as Martin Sleziak, Dominic Michaelis, Lord_Farin, J. M. and julien. You may have already realized that most of us disagree with your opinion on retag, so maybe you should reconsider your opinion.
– 23rd
May 20 '13 at 5:15