positive definite matrix

In order to obtain numerical solution of problemsthat involves a hyperelastic material model, we use what is known as incremental/iterative solution techniques of Newthon's type. The basic idea is to contruct a discrete system of nonlinear equation, KU=F, and solving it using a Newton's method or a modified version of it. As we know, its lead to a systematic linearization of the internal force vector and by the chain rule to the linearization of the material model.