Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook