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Keywords:
semiconvexity; rank 1 convexity; polyconvexity; convexity; rotational invariance
semiconvexity; rank 1 convexity; polyconvexity; convexity; rotational invariance
Summary:
Let $f$ be a function defined on the set ${\mathbf M}^{2\times 2}$ of all $2$ by $2$ matrices that is invariant with respect to left and right multiplications of its argument by proper orthogonal matrices. The function $f$ can be represented as a function $\tilde{f}$ of the signed singular values of its matrix argument. The paper expresses the ordinary convexity, polyconvexity, and rank 1 convexity of $f$ in terms of its representation $\tilde{f}.$
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