Question

Hessian matrix at saddle point

Answer 1

If you're given a bunch of matrices and asked to recognise which one is a saddle point, how do you know? What are the characteristics of a Hessian matrix at saddle point?

Answer 2

I think for a 2 x 2 matrix there is a simple test
for higher dimensions, not so easy.

Answer 3

To me, if the size of the matrices is up to 5x5, we can figure out by their determinants. If it is > 5, we have to use math tool to define it.

Answer 4

@phi what would it be for a 2x2 matrix?

Answer 5

If the determinant < 0 you have a saddle point
if positive, it's a min or max: fxx > 0 -> min, fxx < 0 -> max
for what it is worth,
http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-10-second-derivative-test/

though the Professor does not speak in terms of Hessian matrix

extending the idea to 3 x 3
https://www.quora.com/What-is-the-Hessian-matrix