Sobre funciones vectoriales cuadráticas y sus gradientes

In this article, we discuss the quadratic vector function $\phi(x) = \frac{1}{2}x^T A x + x^T b + c$, first with real entries and then presenting its version with complex entries. Since it is known that the gradient of the real version is essentially the symmetric part of the matrix $A$, this article proposes a notion of the gradient of a vector function such that the gradient of a complex quadratic vector function is also essentially the hermitian part of the corresponding complex matrix $A$.