# Linear algebra and linear equations are sometimes confused

It is unfortunate that the term 'algebra' refers to two quite distinct things depending on what level of mathematics you are studying at. While I suppose linear equations such as $$2x+8=12$$ do technically fit within the field of linear algebra, it seems strange to have these elementary equations grouped with questions about vector spaces and matrices. All this shouldn't be too much of a problem, but in the past I have seen new contributors being lambasted for 'using tags that they knew nothing about' when they use the linear algebra tag in place of the polynomials tag. Yes, they probably should have read the tag description, but it does a little unreasonable to expect someone to do everything perfectly from the moment they ask their first question on this site.

With this in mind, I ask whether a linear equation tag would be helpful to distinguish the two. Something that says 'not to be confused with linear algebra', and clarified what the distinction between the two areas is, would seem very worthwhile to me. While linear equations do fall under the broader polynomial tag, there is a distinct tag for quadratics, and so it seems sensible to have one for linear equations as well. When I first learnt about linear equations in school, it must have been $$5$$ years before I knew what a polynomial was. Tagging should help, not hinder people who are trying to learn. As much as possible, tagging should be appropriate to the level of mathematics that someone is working at.

• Lambasted? If you see someone being lambasted in a comment about the tags they used, please do flag the comment as "Unfriendly or unkind". Commented Aug 7, 2020 at 3:29
• Tagging those question (algebra-precalculus) will suffice IMO. Commented Aug 7, 2020 at 5:30
• I've seen users use the algebraic-geometry tag for questions about the equation of a circle (presumably because equation implies algebra, and circle implies geometry). The occasional mistagging of a question is inevitable. Commented Aug 7, 2020 at 6:41

I think the status quo is fine.

Linear systems of equations can belong in either algebra-precalculus or linear-algebra, depending on the techniques and tools the student knows and is expected to use. A linear-equations tag would probably draw traffic from the whole spectrum (not only about $$2x+8=12$$ but also about how to solve large sparse systems when the matrix is not positive-definite, etc).

We could have a single-linear-equation tag but at that point it's unlikely a new user will find or use the tag.

So I think the best approach is to keep things as they are and (politely!!) re-tag questions as algebra-precalculus as appropriate.

PS: wouldn't it be great if, in this age of machine learning, the Math.SE software automatically classified questions based on the question content text, and warned users about potentially misused tags?

• Ha, I think machine learning would be the best solution! I understand your point—it just seems a little unfortunate that people can mis-tag a post and then be criticised for it. But, hey, most of the contributors here are fairly welcoming to new users, and so I suppose I shouldn't worry too much about it.
– Joe
Commented Aug 15, 2020 at 0:46
• In the last paragraph you mentioned that software could automatically suggest tags and that also it could provide tag warnings. Here is an older post concerning suggestions of tags: What about suggested tags feature? There is also a thread about warnings: Do we want tag warnings, and for which tags? I hope it will become easier if/when this is implemented: Give moderators the power to add tag warnings. Commented Aug 15, 2020 at 8:25