The hessian H of a n-variable
function f is a n by n
matrix whose (i,j)-th entry is the second
order partial derivative:
2
d
H(i,j) = ------ f(x ,x ,...,x )
dx dx 1 2 n
i j
The hessian is
symmetric only if the corresponding partial
derivatives are
continuous. If it is the case, one can gain
insight into the
behavior of f at a given point a=(a1,a2,...) by computing the
determinant of its hessian. For example, if the determinant of the hessian is negative, then a is a
saddle point of f. The hessian was introduced by
german mathematician
Ludwig Otto Hesse in 1842.
See also Jacobian matrix.