Created Friday 15 November 2013
- http://home.bi.no/a0710194/Teaching/BI-Mathematics/GRA-6035/2010/lecture5-hand.pdf
- http://www.economics.utoronto.ca/osborne/MathTutorial/CVNF.HTM
- http://www.math.vt.edu/people/dlr/m2k_svb11_hesian.pdf
The hessian matrix is used to classify CritialPoints
In 2D, the hessian matrix of a function f is
`H(f) = ((f_(x x), f_(xy)),(f_(yx), f_(yy)))`
where `f_(xy)` is the derivative of `f_x` with respect to y.
Ex: `f(x,y) = x^2 - y^2 - xy`
- `f_x = 2x - y`, `f_y = -2y - x`
- `f_(x x) = 2`, `f_(xy) = -1`
- `f_(yy) = -2`, `f_(yx) = -1`
`H(f) = ((2, -1), (-1, -2))`
Properties of Hessian
- the Hessian is always symettric H(f)* = H(f) (Not sure what * does)
- negative semidefinite matrix is a Hermitian matrix all of whose eigenvalues are nonpositive.