申論題

(d) (2+3%) Consider the vector space R^2✖2 with the inner product (A,B):= trace(A^TB) and denote Y:= .(i) Describe Y^⊥ as the span of an orthonormal basis. (ii) What is the matrix, denoted by P_Y⊥, that represents the orthogonal projecting operation Ⅱ_Y⊥ : R^2✖2 → Y^⊥ along with the subspace Y with respect to the ordered basis E = {G,H}, where G and H are vectors of the standard bases for Y and Y^⊥, respectively?