Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dot product between grad f and an arbitrary vector

  1. Aug 17, 2008 #1
    Given a function f: R^n -> R, a point x in R^n, and an arbitrary vector v in R^n - is the dot product between grad f and v (evaluated at x) the same as df/dv?

    If yes, it would be great if someone were to demonstrate a proof.

    If no, what should be the correct interpretation of the dot product?
     
  2. jcsd
  3. Aug 17, 2008 #2

    Defennder

    User Avatar
    Homework Helper

  4. Aug 17, 2008 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The first thing you will have to do is define df/dv! I know, for example, Dvf as the directional derivative Defennder refers to- the rate of change of f in the direction of v which is independent of the length of v. The dot product of grad f with an arbitrary unit vector is the derivative in that direction. The dot product of grad f with an arbitrary vector is the derivative in that direction multiplied by the length of the vector.
     
  5. Aug 17, 2008 #4
    Thanks for the links! It makes sense now.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Dot product between grad f and an arbitrary vector
Loading...