| 1. | The Lie derivative of a scalar is just the directional derivative:
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| 2. | The directional derivative provides a systematic way of finding these derivatives.
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| 3. | Note that in many optimization applications, the directional derivative is indeed sufficient.
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| 4. | The covariant derivative is a generalization of the directional derivative from vector calculus.
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| 5. | The directional derivatives are still locally in L " p ".
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| 6. | It can be used to calculate directional derivatives of scalar functions or normal directions.
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| 7. | This is an extension of the directional derivative to an infinite dimensional vector space.
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| 8. | You may find directional derivative interesting, though.
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| 9. | Would it be more correct to use the term directional derivative instead of gradient?
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| 10. | The Fr�chet derivative allows the extension of the directional derivative to a general Banach space.
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