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Let $f(x):\mathbb R^n \to \mathbb R$ be a smooth function, and let $f(0)=0$.

I alway see that someone rewrite the function in the form $f(x)=x_1b_1(x_1)+x_2b_2(\overline {x_2})+...+x_nb_n(\overline x)$,

where the $\overline {x_i}=[x_1\ \ x_2\ \ ...\ \ x_i]^\mathrm{T}$

Can someone provide a proof?

  • 0
    If $x_2\neq 0, x_3\neq 0$, we can't verify $b_1(x_1)$ has variable $x_1$ and $b_2,b_3,\cdots$ ??2011-02-11

0 Answers 0