Gradient Vector Field
In the presence of a Riemannian metric or a symplectic form, to every smooth function is associated a vector field (the gradient or Hamiltonian vector field). These vector fields vanish exactly at the critical points of the original function, and thus the critical points are stationary, i.e. constant trajectories of the flow associated to the vector field.
Read more about this topic: Critical Point (mathematics)
Famous quotes containing the word field:
“Give me the splendid silent sun
with all his beams full-dazzling,
Give me juicy autumnal fruit ripe and red from the orchard,
Give me a field where the unmow’d grass grows,
Give me an arbor, give me the trellis’d grape,
Give me fresh corn and wheat, give me serene-moving animals teaching content,”
—Walt Whitman (1819–1892)