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We prove that $F$ is invertible if $m = n$ and $\\sum^{d-1}_{i=1} JF(\\alpha_i)$ is invertible for all $i$, which is trivially the case for invertible quadratic maps. More generally, we prove that for affine lines $L = \\{\\beta + \\mu \\gamma | \\mu \\in C\\} \\subseteq C^n$ ($\\gamma \\ne 0$), $F|_L$ is linearly rectifiable, if and only if $\\sum^{d-1}_{i=1} JF(\\alpha_i) \\cdot \\gamma \\ne 0$ for all $\\alpha_i \\in L$. This appears to be the case for all affine lines $L$ when $F$ is injective and $d \\le 3$. 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