HI to all!
I've a math question about the Hessian Matrix. I know that it's used for clasify critical points of a 3-D function, but what happens if the Hessian is undefined (Hessian = 0) in a point?... How i can analyze the critical point?...
A particular sample is: f(x,y) = (y-x)^2*(y+x).
The gradient vector of this function is: grad(f)= [ 3x^2 - 2xy - y^2 , -x^2 - 2xy + 3y^2 ]. To find critical points we have to do grad(f)=0 (vector). And in this case it's easy to verify that the critical points lie in the Y=X line.
In this case the analysis of the Determinant of the Hessian Matrix (Fxx*Fyy-Fxy^2) gives 0 for the points of this line. So how can I continue the analysis, without using maple?. Is there a method for analizing these special cases?
Thanks in Advance!