Difference between revisions of "Talk:Addition of vector spaces"
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:: Ah, yes, I see: I should look at the notes... [[User:Boris|Boris]] ([[User talk:Boris|talk]]) 18:30, 18 March 2016 (UTC) | :: Ah, yes, I see: I should look at the notes... [[User:Boris|Boris]] ([[User talk:Boris|talk]]) 18:30, 18 March 2016 (UTC) | ||
| − | (Edit conflict) However, the (linear) operations are not specified here in the {{M|K}}-indexed case; the written object is just the | + | (Edit conflict) However, the (linear) operations are not specified here in the {{M|K}}-indexed case; the written object is just the [[Cartesian product]] of ''sets'' {{M|V_i}}, defined elsewhere. Here the point should be, how to turn the product (defined elsewhere) into a vector space. [[User:Boris|Boris]] ([[User talk:Boris|talk]]) 18:23, 18 March 2016 (UTC) |
Revision as of 18:55, 18 March 2016
About the alternative form of the external direct sum: I'd say, [ilmath]f[/ilmath] and [ilmath](u_1,\cdots,u_n)[/ilmath] are already two alternative forms of the same object (or else, what the tuple is?); and if so, then this remark is not needed in this article. Just imagine that we always list all combinations of all known alternative forms of all subexpressions of a given expression... Boris (talk) 18:12, 18 March 2016 (UTC)
Oops, no, I should read more! This is a preparation to the following [ilmath]K[/ilmath]-indexed case. Boris (talk) 18:15, 18 March 2016 (UTC)
- This was put on hold until I could unify several definitions, I still haven't worked it out (see Notes:Vector space operations) it is lacking. Writing things in the main namespace is a commitment, I was premature there. I'd love some guidance on the issue. Alec (talk) 18:19, 18 March 2016 (UTC)
(Edit conflict) However, the (linear) operations are not specified here in the [ilmath]K[/ilmath]-indexed case; the written object is just the Cartesian product of sets [ilmath]V_i[/ilmath], defined elsewhere. Here the point should be, how to turn the product (defined elsewhere) into a vector space. Boris (talk) 18:23, 18 March 2016 (UTC)
