Mathematics Homework Help. California State University Application of the Taylor Expansion Theorem Question
Find the gradient and hessian of the following functions. [Hint: it would be much easier to use Taylor’s Expansion Theorem f(x+d) = f(x)+ ∇f(x),d+ 1 2d∇2f(x)d+···, where f : Rn → R, x ∈ Rn and d∈Rn.] (a) f(x) = 1 2xTAx where A is an n×n symmetric matrix and x ∈ Rn. (b) f(x) = 1 2y−Ax22 where y ∈ Rm, A∈Rm× n, and x∈Rn.
