1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Numerical Range
  1. Finding the Range? (Replies: 18)

  2. Numerical Range (Replies: 1)

  3. Range Question (Replies: 9)

  4. Ranges of convergence (Replies: 16)

  5. Range of graphs (Replies: 1)

Loading...