"In vector calculus, and its generalizations in differential geometry, the gradient is a differential operator generalizing the derivative that acts on differentiable (scalar) functions, producing vector fields. The gradient of a function at a point is a vector that encodes the direction in which the function increases the most rapidly as well as the rate of increase. The divergence of a function is a special case of the Jacobian."
I've corrected my post in meta---thanks for the catch.
The scope of the proposal as written includes just the vector calculus gradient operator and its immediate generalization in Riemannian geometry, but that I proposed that scope is at least partly a function of my familiarity with the differential geometric sense of the term and relative unfamiliarity with the functional analytic sense.
(NB there's an extant tag, gradient-descent, that already applies to at least some of the latter.) That said, I don't immediately see any harm in expanding the scope of the proposed gradient tag to include that lattermost sense.
