1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Derivative matrices

  1. Mar 12, 2009 #1
    1. The problem statement, all variables and given/known data
    Suppose that the mapping F:Rn[tex]\rightarrow[/tex]Rm is continuously differentiable and that there is a fixed mxn matrix A so that
    DF(x)=A for every x in Rn.

    Prove that then F is a mapping such that F(x)=Ax+c for some c[tex]\in[/tex]Rm

    2. Relevant equations

    DF(x)ij= [tex]\partial[/tex]Fi(x)/[tex]\partial[/tex]xj (the ijth entry of the derivative matrix)

    3. The attempt at a solution
    I tried to solve this with the first-order approximation F(x)=F(xo)+F´(xo)(x-xo) +[tex]\epsilon[/tex](x-xo)||x-xo||

    Where [tex]\epsilon[/tex](x-xo)||x-xo|| approaches naught.
    But it didn't amount to anything sensible and I'm not sure what to do... What should I try next?
     
  2. jcsd
  3. Mar 12, 2009 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Actually, when you write F´(xo)(x-xo) like in a Taylor series, you mean
    DF(xo) . (x-xo)
    which is a multiplication of a matrix by a vector. You know that DF(xo) = A... if your expansion is otherwise correct that should enable you to actually identify c explicitly.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Derivative matrices
  1. The Matrices (Replies: 12)

Loading...