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試卷名稱：106年 - 106 國立中山大學_碩士班招生考試_電機系(乙組)：工程數學乙#125249
年份：106年
科目：中山◆電機◆工程數學乙
14. Let E := {
be a basis of 
and F := 
⊂ 
with the property 
= 1,…,n uᵢᵀvⱼ = 1 when i = j, and 
= 0 when i ≠ j. Which of the following statements are true?
(A) F is also a basis of 
, and the coordinate vector of any x ∈ 
with respect to base F is 
(B) Any x ∈ 
can be represented as x = c₁u₁ + ... + 
= 
for each i.
(C) Denote the transition matrix from base E to base F by S. Then S(i, j) = 
, for i, j = 1,…, n.
(D) The transition matrix from base F to base E can be described by (
), where 
denotes the coordinate vector of 
with respect to base E.
(E) Denote U := 
and V := 
. Then Ux = λx for some x ≠ 0 iff 
, where the upper bar means to take the complex conjugate.
