92 - The Hessian

Local Linearization generalizes the idea of the tangent plane to any multivariable function. The idea is to approximate a function near some point with a simpler function that hasthe same value at that point, as well as the same partial derivatives.

Let be some multivariable function. Let denote a vector containing each component of the function minus the value for each component at that point.
then the local linearization of around the point is defined