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When is the Jacobian of a function a diagonal matrix

  1. Mar 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Let f(x,y,z)=(exp(x),cos(y),sin(z)).Compute the Jacobian J(f) of f . In general ,when will the Jacobian J(g) of a function g(x,y,z) be a diagonal matrix ?


    2. Relevant equations



    3. The attempt at a solution
    I am not quiet sure about this question
    for J(f) i found that
    (e^x 0 0)
    (0 -siny 0)
    (0 0 cosz)
    and i think this is already a diagonal matrix
     
  2. jcsd
  3. Mar 18, 2009 #2

    Mark44

    Staff: Mentor

    Re: Jacobian

    Your Jacobian looks fine to me. The second question was "In general ,when will the Jacobian J(g) of a function g(x,y,z) be a diagonal matrix ?"

    What was it about the component functions that gave you all those zeroes off the diagonal?
     
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