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Flashcards in Unit 4 Deck (8)
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1
Q

Note

A

Gradient is a vector valued function with domain and codomain in R^n

2
Q

Necessary condition for there to be a minimum at x*?

A

The FOC is satisfied (=0n)

3
Q

Pulling it all together: solution method? (2 steps and 2 hessian outcomes)

A

1) find any critical points
2) obtain hessian matrix H(x)

If hessian is PD for ALL x, objective function is combs and any critical point yields a unique global minimum

If hessian is PD at x* (but not all x) then there is a strict local minimum at x*

4
Q

Note:

A

Revise first year matrix work (eg. Cramer’s rule) for simplicity

5
Q

See notes

A

Subscript notation or partial derivatives

6
Q

What do Taylor’s polynomials do?

A

They use Taylor’s theorem to give information about a function f in the REGION of a chosen point (ie. x*), however it sacrifices ‘global’ info about f

7
Q

With Taylor polynomials, what should you do if possible?

A

Put your answer in a form so the bit in the brackets are all the same factors (see class 3 question 1)

8
Q

Quick way to identify if symmetric 2x2 matrix is positive definite?

A
Given A= a  b
                 b c
If a>0 and ac>b^2 then matrix A is positive definite (know from class 2)