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?

Please Help.

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- Mar 27th 2013, 07:45 PMmrmaaza123Smallest 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?

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

Hint for this question: What is $\displaystyle \mathrm{span}\,\{1,i\}$? - Mar 28th 2013, 07:07 PMmrmaaza123Re: 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 AMNehushtanRe: Smallest generating set
The point is that $\displaystyle \mathrm{span}\{1,i\}$ is as big as it can be – so adding more elements to the spanning set won’t make a difference. (Smile)