Hessian

[AJ]

f: R^n to R ... twice differentiable, concave and homogeneous of degree 1.
Its hessian is:

Neg. Definite
Postive Def.
SIngular
Non-singular


Answer in key is singular.. can somebody explain..

[aditi5000]

AJ the function is HOD 1. differentiate it and it becomes HOD 0. So the hessian (of 2nd order derivatives) must be zero.. ie singular. I'm not sure about this.

[ritu]

hi aditi even i thought the same as u....hod 1 means function was linear???
second diff wud definitely be zero nd the crosd partial derivative will also be zero....so that means singular...
pls correct us if its wrong...

[Chinni18]

I figured it the same way Ritu and aditi. I think we are on the right track