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Numerical Range

  1. Sep 1, 2007 #1
    1. The problem statement, all variables and given/known data

    Hi, I have a question: Prove that a square matrix of order n has an LU-factorization if and only if the origin is not contained in the numerical range.

    2. Relevant equations

    The numerical range is found using the Euclidean inner scalar product <Ax,x> where <x,x>=1 and. The numerical range is A(W)=(<Ax,x> such that <x,x> =1 for all x reals)

    3. The attempt at a solution

    I tried considering the 2x2 matrix case but got stuck.:) Thanks in advance!
  2. jcsd
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