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!

Proving a Theorem, related to Gerschgorin

  1. Sep 21, 2011 #1

    syj

    User Avatar

    1. The problem statement, all variables and given/known data
    Here is the theorem I need to prove:

    For A=(aij)[itex]\in[/itex]Cnxn

    we have

    p(A)[itex]\leq[/itex][itex]max_{i}[/itex][itex]\Sigma^{n}_{j=1}[/itex]|aij|


    2. Relevant equations



    3. The attempt at a solution
    I have no idea how to go about this. :cry:
     
  2. jcsd
  3. Sep 21, 2011 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Some definitions might be nice.
    What is [itex]C_{n \times n}[/itex]? What is [itex]p(A)[/itex]? What does i run over?
     
  4. Sep 21, 2011 #3

    syj

    User Avatar

    Sorry,
    Cnxn is the set of nxn matrices with entries in the complex number system.

    p(A)= max{|[itex]\lambda[/itex]1|, |[itex]\lambda[/itex]2|, ...}

    p(A) is the smallest circle in the comple plane, centered at the origin, which contains all the characteristic values of A.
     
  5. Sep 21, 2011 #4

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Maybe it's a good idea to start with the simple case, where A is diagonalizable.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proving a Theorem, related to Gerschgorin
  1. Theorems prove (Replies: 2)

  2. Proving simple theorem (Replies: 2)

Loading...