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Homework Help: Symmetric matrix problem

  1. Mar 18, 2009 #1
    1. The problem statement, all variables and given/known data
    consider the 2*2 symmetric matrix A =
    (a b )
    (b c)
    and define f: R^2--R by f(x)=X*AX . show that [tex]\nabla[/tex]f(x)=2AX

    2. Relevant equations



    3. The attempt at a solution
    quiet confuse about this question
    [tex]\nabla[/tex]f(x)=(1. The problem statement, all variables and given/known data
    consider the 2*2 symmetric matrix A =
    (a b )
    (b c)
    and define f: R^2--R by f(x)=X*AX . show that [tex]\nabla[/tex]f(x)=2AX

    2. Relevant equations



    3. The attempt at a solution
    quiet confuse about this question
    [tex]\nabla[/tex]f(x)=(diff(f, x) , diff(f,y) )
    can i set L=(u,v) to prove L is a linear map?
     
  2. jcsd
  3. Mar 18, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    Re: question

    I think it could be your notation, do you mean:

    [tex] f:\Re^2 \rightarrow \Re [/tex]
    [tex] f:\textbf{x}\rightarrow z [/tex] for [tex] \textbf{x}=(x,y) \in \Re^2, z \in \Re[/tex]

    with f defined by
    [tex] f(\textbf{x}) = z = \textbf{x}^T \textbf{.A.x}[/tex]
    if unsure how about multiplying this out based on your matrix?

    then what is
    [tex]\nabla f(\textbf{x})[/tex]?
     
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