Smallest generating set

• Mar 27th 2013, 07:45 PM
mrmaaza123
Smallest generating set
Let W = span {1,i,1+i,1-i} over R. Find the smallest generating set for W ?

I don't understand how to solve this question. Is there some particular way for finding the smallest generating set?

• Mar 28th 2013, 06:35 AM
Nehushtan
Re: Smallest generating set
In other words, find a set $S$ such that $W=\mathrm{span}\,S$ and $W\ne\mathrm{span}\,T$ for any proper subset $T$ of $S$.

Hint for this question: What is $\mathrm{span}\,\{1,i\}$?
• Mar 28th 2013, 07:07 PM
mrmaaza123
Re: Smallest generating set
I believe the span of {1,i} is C(R). But i don't understand how that helps ?
• Mar 30th 2013, 09:19 AM
Nehushtan
Re: Smallest generating set
The point is that $\mathrm{span}\{1,i\}$ is as big as it can be – so adding more elements to the spanning set won’t make a difference. (Smile)