Hessian,
n. 1. also called Hessian matrix. the matrix of which the entries are the second partial derivatives of a given function; for example, the Hessian of f(x, y) = x2 - y2 is
The analogue of the second derivative test for functions of more than one variable uses the Hessian to identify locally optimal values of the function: the Hessian is positive definite at a local minimum, negative definite at a local maximum, and indefinite at a saddle point; if it is singular, the test is indeterminate. 2. the determinant of the Hessian matrix. (Named after the German differential geometer Ludwig Otto Hesse (1811-74).)
The analogue of the second derivative test for functions of more than one variable uses the Hessian to identify locally optimal values of the function: the Hessian is positive definite at a local minimum, negative definite at a local maximum, and indefinite at a saddle point; if it is singular, the test is indeterminate. 2. the determinant of the Hessian matrix. (Named after the German differential geometer Ludwig Otto Hesse (1811-74).)