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

Chosing normalization

  1. Sep 1, 2011 #1
    I have a 40*40 matrix which has elements very close to 1 on diagonal and very small off-diagonal elements.
    I find determinant of many of these randomly generated matrix, determinant is roughly multiplication of diagonal matrix squared. As (.95)^40 is a small number and (1.05)^40 is a bignumber, I get a histogram that increases from zero reaches a maxima and then fall to zero when I plot all these determinant values. It has a mean of 1 but peak at around .1

    What kind of nomalization should I use such that when I make histogram it looks like a bell curve with a mean of 1.
  2. jcsd
  3. Sep 1, 2011 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    Are you using the term "normalization" to refer to a change of variable meets very specific technical requirements or would you be happy with "any old change of variable"?

    You could histogram the logarithms of the determinant values. That might be bell shaped. You would probably have to add some constant to the logs to get the mean to be 1.
  4. Sep 3, 2011 #3
    If you mean D~Prod(1+eps.Bjj) or D~Prod(1+eps.Bjj)^2 where B is a random matrix, that would be approximately lognormal (use CLT on log(D)).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook