Definition talk:Generated Submodule/Linear Span

The definition is equivalent to two others, similar to what is done for Definition:Closed Linear Span. --Lord_Farin 10:05, 4 January 2012 (CST)


 * Hm, GFP, be sure that you understand that the notion of Linear span can be associated to any set of vectors in $n$-space. If this set is finite, then the sum indeed can be taken over all elements. However, to only define the span of $n$ elements in $n$-space is too narrow. Please modify it or reply. --Lord_Farin 03:11, 30 January 2012 (EST)


 * I've only come across it with finite vectors, Good now? --GFauxPas 06:29, 30 January 2012 (EST)


 * Revisiting the issue now that my class addressed infinite sets. Why can't we define the span as the set of all linear combos of the set, i.e., every linear combo of a finite sequence of vectors in the space? --GFauxPas 11:11, 20 April 2012 (EDT)

Can $A = \varnothing$? I don't see how that would work. It's related to my question here, because if a subspace has to be non-empty then how can we say Linear Span is Linear Subspace if $A$ might be empty? --GFauxPas 15:01, 11 March 2012 (EDT)


 * Don't forget the empty sum. By default, it equals the identity element of addition. This might deserve explicit statement on the proof page, though. --Lord_Farin 19:01, 11 March 2012 (EDT)