课程名称︰线性代数二
课程性质︰数学系大一必修
课程教师︰余正道
开课学院：理学院
开课系所︰数学系
考试日期︰2020年06月05日(五)
考试时限：11:20-11:50，共30分钟
试题 :
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