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Math Help - subtraction of vector subspaces??

  1. #1
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    subtraction of vector subspaces??

    I know that subtraction of vector subspaces is not defined.

    Lets have two subspaces A and B such that A+B=C.
    I would like to have A' such that A' \oplus (A \cap B)=A and A' \oplus B=C.

    In other words, A' \cap B=0, (A + B)=(A' \oplus B)

    As example, let say that the vectors [a1,a2,a3] form a basis of A, and the vectors [b1,b2] are a basis for B. Now, let say that it's possible to form the vector a3=v1*b1+v2*b2, where v1 and v2 are scalars, but it's not possible to obtain a1 nor a2 from linear combinations of b1 and b2. Then a basis of (A \cap B) would be a3, and a basis of A' would be [a1,a2]. A basis for C would be [a1,a2,b1,b2].

    Is this operation defined in vector space algebra? which symbol to use? This is a sort of substraction A'=A-(A \cap B) but I don't know how to write it properly.
    Last edited by palam81; December 2nd 2011 at 09:57 AM.
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