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Homework Help: Inverse Function Theorem

  1. Jan 25, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove or Disprove: A 2x2 matrix [tex]\epsilon A+I[/tex] has a cube root near [tex]\left( \begin{array}{cc} 2 & 0 \\ 0 & -5 \end{array} \right)[/tex].

    2. Relevant equations
    Inverse Function Theorem

    3. The attempt at a solution
    I'm just confused about the "near [tex]\left( \begin{array}{cc} 2 & 0 \\ 0 & -5 \end{array} \right)[/tex]" bit. Is this the matrix [tex]A[/tex]? Or is it the matrix [tex]H[/tex] in the derivative [tex]Df(A)(H)[/tex] of the function [tex]f(A)=A^3[/tex]? Otherwise I know what to do.
    Last edited: Jan 25, 2009
  2. jcsd
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