申論題

4.(14%)下面的問題共有二個子題,只要簡短扼要地回答提問即可,不須寫出答案背後的推 導。
 Let V be a vector space with dim(V) = n and an ordered basis E := [x₁, ..,x_n].Let F := [y₁,... , Y_n] be the ordered orthonormal basis generated from basis E by applying the Gran- Schmidt Orthogonalization Process. For any, let [v]_Eand [v]_F denote the coordinate vectors of v with respect to bases E and F, respectively. Let T denote the transition matrix from basis E to basis F. Let L : , ie. L is a linear operator mapping V into itself, and suppose that
Let's denote the matrix representation of L with respect to basis E by A.