Show that a search direction chosen as the solution of the linear system
\mB \vp = -\vg
is a descent direction where when is symmetric, positive definite.
Either of:
\vg^T \vp = -\vp^T \mB \vp < 0
after substituting
or
\vg^T \vp = -\vg^T \mB^{-1} \vg < 0
after substituting .