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