or Jacobian determinant, n. a function derived from a set of n simutaneous equations in n variables, of which the value at any point is the n × n determinant of the Jacobian matrix of partial derivatives of those equations evaluated at that point. If
u_j = f_j(x₁, x₂,..., x_n),
this is generally written If the Jacobian is non-zero, the equations have a non-trivial solution.