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!

Arithmetic and Geometric Mean

  1. Apr 30, 2012 #1

    I have the following equation:


    where lambdas are the eigenvalues of an N-by-N circulant matrix A.

    I used two properties to bound the above equation:



    Are these two bounds correct?

  2. jcsd
  3. Apr 30, 2012 #2


    User Avatar
    Science Advisor
    Gold Member

    The first one is a a statement that the arithmetic mean bounds the geometric mean (true).

    The second is false - simple example: 2 terms on the left 1 + 2 = 3. Right side is 1/(1+1/2) = 2/3.
  4. May 1, 2012 #3
    But we have the identity for the trace that:


    or it just works for k>=1?
  5. May 1, 2012 #4


    User Avatar
    Science Advisor
    Gold Member

    I am not familiar with the trace equation, but as my example shows, what you propose is just wrong. It may be that your guess is correct, k is positive integer.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook