Question: answer the question Let W be a nitedimensional complex inner product space and let S: W > W be a linear map. Assume that S

answer the question

Let W be a nitedimensional complex inner product space and let S: W > W be a linear map. Assume that S = 5*. (i) Show that, for all to E W, the complex number (S [w],w) is real (in other words, its imaginary part equals 0). (ii) Show that S = 0 if and only if (S[w],w) : 0 for all to E W. Hint: Consider (Sh) + 'w],v + w)

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