11. This leads to the Jacobian matrix ". 12. Then the Jacobian matrix of is an matrix, usually defined and arranged as follows: 13. Is an element of the Jacobian matrix . 14. Where, stands for the Jacobian matrix of, and the clear circle denotes function composition. 15. For a real-valued function of several variables, the Jacobian matrix reduces to the gradient vector. 16. If =, then is a function from to itself and the Jacobian matrix is a square matrix. 17. The algorithms proceed either from an analytic specification of the Jacobian matrix or directly from the problem functions. 18. This coefficient matrix of the linear system is the Jacobian matrix ( and its inverse ) of the transformation. 19. He wrote early computer software automating iterative evaluation of direct computer models through a Jacobian matrix of complex numbers. 20. If the Jacobian matrix of the transformation is everywhere a scalar times a rotation matrix, then the transformation is conformal.
