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!

Positive definite function,semi-definite functions

  1. Nov 2, 2012 #1
    Hello all!
    *please explain the terms 'positive definite function' and 'semi-definite function'.*
    I am reading a book on the stability analysis of non-linear models.
    In the chapter for 'neighborhood stability analysis',I came across the "Lyapunov function V".

    V has the following properties:
    1.V is positive definite.
    2.dV/dt is negative semi-definite(stable valley)
    3.dV/dt is positive semi-definite(unstable valley)

    I understand the usual hilltop valley visualization,but please explain the terms 'positive definite function' and 'semi-definite function'. Any level of math is understandable.
    **Is there a connect between 'positive definite function' and 'positive definite matrix'?**
    Last edited: Nov 2, 2012
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

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