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)

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)