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*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'?**

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# Positive definite function,semi-definite functions

Can you offer guidance or do you also need help?

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