Let $E$ be a finite set. Let $K$ be a valued field with valuation in $\mathbb R\cup\{\infty\}$, let $K_0\subset K$ be a subfield on which the valuation is zero on $K_0^\times$, and let $L\subset K^E$ be the scalar extension of a linear subspace $L_0\subset K_0^E$. Let $M(L)$ be the underlying matroid of the coordinate functionals on $L$. Let $\widetilde{\mathcal B}(M(L))\subset\mathbb R^E$ denote the affine Bergman fan, namely the set of vectors $w\in\mathbb R^E$ such that, for every circuit $C$ of $M(L)$, the minimum of $(w_e)_{e\in C}$ is attained at least twice. Define $\operatorname{Trop}(L)$ as the closure in $\mathbb R^E$ of valuation vectors of nonzero-coordinate points in $(L\otimes_K K')\cap (K'^\times)^E$, where $K'$ ranges over valued field extensions of $K$ with real-valued value group. Then $\operatorname{Trop}(L)=\widetilde{\mathcal B}(M(L))$.