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.
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 $\displaystyle \mathrm{span}\,\{1,i\}$?