Definition talk:Basis (Linear Algebra)

It is not true that a maximal linearly independent subset is always a basis. For vector spaces, this is true. --barto (talk) 09:13, 18 December 2016 (EST)

Okay then, stick a note on the page under a "questionable" template -- I want to revisit the sources here and see whether I have got something inaccurate from them or whether I have made an unjustified assumption. --prime mover (talk) 09:29, 18 December 2016 (EST)

... although looking at the history of edits, it seems it was not my mistake, for once. As the additional statement was not made based on any of the source citations, please feel free to correct this, and put the statement on the page where it is appropriate, and if you feel like it, justify the statements with proofs as necessary. --prime mover (talk) 09:32, 18 December 2016 (EST)

What about splitting this up into Definition:Basis of Vector Space and Definition:Basis of Module? --barto (talk) 05:22, 19 March 2017 (EDT)

I seem to have degraded to one's average layman. Could you remind me of (your take on) the difference? — Lord_Farin (talk) 13:32, 20 March 2017 (EDT)

A basis of a vector space is sometimes (equivalently) defined as a maximal linearly independent set. For modules, we can not. So either:

We don't split and take this equivalent definition as a theorem

We don't split and make an equivalent definition, mentioning that it only holds for vector spaces

Split

I can live with all options. --barto (talk) 14:38, 20 March 2017 (EDT)

Sorry for the delay; I was otherwise occupied. Of these options, splitting seems most in line with house style. It has been the solution of choice for a number of similar problems. — Lord_Farin (talk) 14:53, 26 March 2017 (EDT)

In line with our established house style, I have renamed the redirect pages "Basis (Module)" and "Basis (Vector Space)" to "Basis of Module" and "Basis of Vector Space", on the grounds that these are precisely what the title of the redirect specifies. "Basis (Module)" is not so precise. We also want to restrict the proliferation of redirect pages, for operational reasons -- one of them being that if you start entering e.g. "Definition:Basis" into the "Search ProofWiki" window, there is a limit of the number of helpful pages that appear in the resulting typeahead dropdown. So the fewer identically-operating redirects the better. --prime mover (talk) 05:34, 1 May 2017 (EDT)

and I've just noticed I'm going to have to change the stupid source citations. FTS, life's too short. It's going to have to swing by its delicates. --prime mover (talk) 05:37, 1 May 2017 (EDT)