ME232-LEC13

11 flashcards · Mathematics · by John Viljoen

1. give the 3 lyapunov function criteria:

2. what is the hermitian form?

3. what is the hermitian matrix?

4. what do we know about the eigenvalues of the hermitian matrix?

5. what do we know about the jordan form representation of a hermitian matrix?

6. what do we know about the eigenvectors of a hermitian matrix?

7. how can we bound the min and max eigenvalues of the Hermition matrix?

   Using the rayleigh coefficient:

8. define positive definite for complex matrices:

9. define positive semi-definite for complex matrices:

10. give the 3 conditions, only 1 of which must hold for a hermitian matrix to be positive definite:

    if there is a zero for min eigenvalue for 1. then we have positive semidefinite.

11. give the principal minors of: