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Variational calculus proof

  1. Mar 16, 2008 #1
    1. Suppose f:R[tex]^{NxN}[/tex] is defined by f(x,y) = [tex]\varphi[/tex](x) + [tex]\varphi[/tex]*(Ax+y) where [tex]\varphi[/tex][tex]\epsilon[/tex][tex]\Gamma[/tex](R[tex]^{N}[/tex]) and A[tex]\epsilon[/tex]R[tex]^{NxN}[/tex] is skew-symmetric.
    Prove that f*(y,x) = f(x,y)


    3. The attempt at a solution
    Information I know:
    Skew-symmetric : A*=-A
    f* computation: f*(y) = sup(x[tex]\epsilon[/tex]R[tex]^{N}[/tex] {<x,y> - F(x)}

    Would really appreciate it if someone would help me start this proof
     
  2. jcsd
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