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Q27Section II (Mathematics)27 of 190

Only the standard Hermitian form is positive definite on C2\mathbf C^2

Which of the functions defines an inner product on C2\mathbf C^2? Let x=[x1,x2]t,y=[y1,y2]tx=[x_1,x_2]^t, y=[y_1,y_2]^t. (i) (x,y)=x1yˉ2(x,y)=x_1\bar y_2. (ii) (x,y)=x1yˉ1+x2yˉ2(x,y)=x_1\bar y_1+x_2\bar y_2. (iii) (x,y)=x1y1+x2y2(x,y)=x_1y_1+x_2y_2.

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