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Rotationally Invariant Rank 1 Convex Functions

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Abstract.

Let fbe a function on the set M n xnof all nby nreal matrices. If fis rotationally invariant with respect to the proper orthogonal group, it has a representation \tilde f through the signed singular values of the matrix argument Å∈ M^nxn.Necessary and sufficient conditions are given for the rank 1 convexity of fin terms of \tilde f .

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Authors and Affiliations

  1. Mathematical Institute of the AV ČR,Žitná 25, 115 67 Prague 1, Czech Republicsilhavy@math.cas.cz, Czech Republic

    M. Šilhavý

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  1. M. Šilhavý
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Accepted 20 December 2000. Online Publication 18 May, 2001.

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Šilhavý, M. Rotationally Invariant Rank 1 Convex Functions. Appl Math Optim 44, 1–15 (2001). https://doi.org/10.1007/s00245-001-0012-z

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  • DOI: https://doi.org/10.1007/s00245-001-0012-z

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