Question: Using the dotting trick if applicable, for the basis 1/sqrt(2)([1,i] T , [1, -i] T ), find the Linear Transformation Matrix of the rotation transform

Using the dotting trick if applicable, for the basis 1/sqrt(2)([1,i]^T, [1, -i]^T), find the Linear Transformation Matrix of the rotation transform given by T(x, y)^T= (-y, x)^T

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