Norm of a Jacobian Matrix

  • Thread starter Buri
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  • #1
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In "Differential Equations, Dynamical Systems and Introduction to Chaos", the norm of the Jacobian matrix is defined to be:

|DF_x|
= sup |DF_x (U)|, where U is in R^n and F: R^n -> R^n and the |U| = 1 is under the sup.
...|U| = 1

DF_x (U) is the directional derivative of F in the direction of U. But I don't understand what this definition means?

Thanks
 

Answers and Replies

  • #2
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The supremum is taken over all unit vectors U.
 
  • #3
273
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Ahh I see, thanks!
 

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