Positive definite function,semi-definite functions

[marellasunny]

Hello all!
*please explain the terms 'positive definite function' and 'semi-definite function'.*
CONTEXT:
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'?**

 

[fresh_42]

In a way there is a connection between the two: https://en.wikipedia.org/wiki/Positive-definite_function