Re: [分析] 幾題高微和線代

[PhysiAndMath (老師說要愛數學)]

※ 引述《paperbattle (跳針猴王)》之銘言：
: 1.請問要如何造一個bijective map f:(0,1)->[1,0]
: 2.Let a_0 = 0 , a_n+1 = 1/(2+a_n) for all n>0
: 已經知道這數列bounded 但不是monotone
: 如何證明a_n收斂?
: 3.Let T_A (X) = AX - XA  , 其中A是可對角化矩陣 A和X都是n階方陣
: 證明T_A可對角化
: 4.Let u:R^2→R be analytic and nonconstant.
: Suppose u_y=u_xx for x,y in R.
: Can the function u have a local maximum point at (x_0,y_0) in R^2?
: Prove or disprove your answer.
: 請高手指點 謝謝

1.
A = {1/2,1/3,.....,1/n,...}
B = {0,1}聯集A
def: g:A->B
     g(1/n)= 1/(n-2) if n>2
     g(1/2)= 0

     h:(0,1)\A -> [0,1]\B
     h(x)=x

     f(x)=g(x) if x belong to A
          h(x) if x belong to (0,1)\A

是這樣吧...

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