課程名稱︰線性代數二
課程性質︰數學系大一必修
課程教師︰余正道
開課學院：理學院
開課系所︰數學系
考試日期︰2020年06月05日(五)
考試時限：11:20-11:50，共30分鐘
試題 :
2
1. Let A = [2 1] ∈M (R), consider A as a linear operator on R equipped with
[1 2] 2
the standard inner product. Evaluate the operator norm of A.
∞ k
2. Let B = [1/2 1/3] ∈ M (R), prove that Σ B exists and compute it
[ 0 1/2] 2 k=0
explicitly.
3. Show that there exists C∈M (C) and ε>0 such that for any self-adjoint
n
matrix S∈M (C), the operator norm ||C-S|| > ε.
n