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Math Help - Linear functional

  1. #1
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    Linear functional

    Let X be n-dimensional vector space. Z a proper substance of X.
    Let x_0 be element of X - Z (complement of Z).

    Show there is a linear functional f on X such that:

    f(x_0)=1 and f(x)=0 for all x element of Z.
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  2. #2
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    Do you know about inner product?
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  3. #3
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    Construct a basis for Z, say \{u_1, u_2, ..., u_n\}. Extend that to a basis for X: \{u_1, u_2, ..., u_n, v_1, v_2, ..., v_m\}.

    Define f(u_i)= 0, f(v_i)= 1, and extend to all of X by "linearity".
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  4. #4
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    thanks for your input

    how do I use the inner product?
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