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Math Help - Smallest generating set

  1. #1
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    Question 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?

    Please Help.
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  2. #2
    Junior Member Nehushtan's Avatar
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    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\}?
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  3. #3
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    Re: Smallest generating set

    I believe the span of {1,i} is C(R). But i don't understand how that helps ?
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  4. #4
    Junior Member Nehushtan's Avatar
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    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.
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