Let $m,n$ be positive integers, and let $f:\mathbb R^{m\times n}\to\mathbb R$ be continuous and quasiconvex in Morrey's sense: for every bounded [open set](/page/Open%20Set) $U\subset\mathbb R^n$, every $A\in\mathbb R^{m\times n}$, and every $\varphi\in W^{1,\infty}_0(U;\mathbb R^m)$,
Then $f$ is rank-one convex in the following sense: for every $A\in\mathbb R^{m\times n}$ and every matrix $B\in\mathbb R^{m\times n}$ with $\operatorname{rank} B\le 1$, the function
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\begin{align*}
g_{A,B}:\mathbb R\to\mathbb R,\qquad g_{A,B}(\tau)=f(A+\tau B)
\end{align*}