申論題 - 阿摩線上測驗

申論題資訊

試卷：103年 - 103 國立中山大學_碩士班招生考試_電機系(乙組)：工程數學乙#110237
科目：中山◆電機◆工程數學乙
年份：103年
排序：0

題組內容

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,... .,x_n].Let

F:=[y₁ , Y_n] be the ordered orthonormal basis generated from basis E by applying the Gram- Schmidt Orthogonalization Process. For any

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 :

, 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.

申論題內容

(c) (6%) Suppose now that and denote X := [x₁,... ,x_n].Let X = QR be the QR factorization of matrix X. Is there any relationship between matrices T, Q and R? If yes, write an equation to describe such a relationship. If no, give a brief explanation for it.