Question: MAT3701 : Consider the inner product space C2 over C with inner product dened by < (u1; u2); (v1; v2) > = u1v1 iu1v2 iu2v1

MAT3701 : Consider the inner product space C2 over C with inner product <; > dened by < (u1; u2); (v1; v2) > = u1v1 iu1v2 iu2v1 3u2v2: (4.1) Show that < (u1; u2); (u1; u2) > > 0 for all (u1; u2) 6= (0; 0) and < (u1; u2); (u1; u2) > = 0 if and only if (u1; u2) = (0; 0). [10] (4.2) Apply the Gram-Schmidt orthogonalization process to f(1; 0); (0; 1)g to construct an orthonormal basis for C2 with respect to given < ; >

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