Abstract
Let f be a function defined on the set M 2×2 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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Šilhavý, M. On Semiconvexity Properties of Rotationally Invariant Functions in Two Dimensions. Czechoslovak Mathematical Journal 54, 559–571 (2004). https://doi.org/10.1007/s10587-004-6408-6
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DOI: https://doi.org/10.1007/s10587-004-6408-6