| 21. | It extends further to differentiable maps between differentiable manifolds, as the points where the rank of the Jacobian matrix decreases.
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| 22. | The earliest approximation was to linearize the nonlinear function and apply the resulting Jacobian matrix to the given mean and covariance.
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| 23. | The Jacobian matrix of f is formed by the four partial derivatives of u and v with respect to x and y.
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| 24. | The topic of multilinear algebra is applied in some studies of multivariate calculus and manifolds where the Jacobian matrix comes into play.
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| 25. | The Jacobian matrix is required by many algorithms that solve the ordinary differential equations numerically, particular when the ODEs are stiff.
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| 26. | The Jacobian matrix is determined iteratively based on the "'secant equation "'in the finite difference approximation:
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| 27. | If the largest real part of the eigenvalues is zero, the Jacobian matrix does not allow for an evaluation of the stability.
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| 28. | Recalling that v is the specific volume, u the flow speed, s the specific entropy, the corresponding jacobian matrix is:
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| 29. | Jacobian matrix consisting of the partial derivatives of " f i " with respect to " X j ":
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| 30. | There is an analogous criterion for a continuously differentiable map with a fixed point, expressed in terms of its Jacobian matrix at,.
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