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Let W be an inner product space and v1,...,vn a basis of V. Show that〈S, T...

  1. Let W be an inner product space and v1,...,vn a basis of V. Show that〈S, T 〉 = 〈Sv1, T v1〉 + . . . + 〈Svn, T vn〉

    for S,T ∈ L(V,W) is an inner product on L(V,W).

  2. Let S ∈ L(R^2) be given by S(x1, x2) = (x1 + x2, x2) and let I ∈ L(R^2) be the identity operator. Using the inner product defined in problem 1 for the standard basis and the dot product, compute 〈S, I〉, ||S||, and || I ||. Please answer problem 2.

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