| 1. | For a more complete description, see Jacobian matrix and determinant.
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| 2. | At the point the rows of the Jacobian matrix are and.
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| 3. | At each timestep the Jacobian is evaluated with current predicted states.
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| 4. | This method uses the Jacobian matrix of the system of equations.
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| 5. | The pattern of lines of curvature is determined by the Jacobian.
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| 6. | However, computing this Jacobian is a difficult and expensive operation.
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| 7. | That is, the determinant of the Jacobian of the transformation.
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| 8. | We can also express this compactly using the Jacobian determinant:
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| 9. | Instead a matrix of partial derivatives ( the Jacobian ) is computed.
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| 10. | The Jacobian determinant is occasionally referred to as " the Jacobian ".
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