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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Do you know about inner product?
Construct a basis for Z, say . Extend that to a basis for X: .
Define , , and extend to all of X by "linearity".
how do I use the inner product?
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