Am I correct in thinking the Hessian essentially gives you a sense of the local curvature of the function?
Max
Yep! A positive definite Hessian implies the function is curving 'up' (and e.g. if the gradient is zero, you're at a local minimum), negative definite implies curving 'down', and semi-definite implies that the function is constant along some direction.
rmvenkat
How do we prove the expression for the multivariate case? Or did we do it earlier ?
Am I correct in thinking the Hessian essentially gives you a sense of the local curvature of the function?
Yep! A positive definite Hessian implies the function is curving 'up' (and e.g. if the gradient is zero, you're at a local minimum), negative definite implies curving 'down', and semi-definite implies that the function is constant along some direction.
How do we prove the expression for the multivariate case? Or did we do it earlier ?