4.(26%)下面的問題共有四個子题,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,... .,xn].Let F:=[y1 , Yn] be the ordered orthonormal basis generated from basis E by applying the Gram-Schmidt Orthogonalization Process. For any

denote the coordinate vectorsof v with respect to bases E and F, respectively. Let T denote the transition matrix from basis E tobasis F. Let L :

, i.e. 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.
【題組】(a) (6%) Write an equation to indicate the relationship between the two coordinate vectors[L(v)]E and [v]F.