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Applied Mathematics and Optimization

, Volume 44, Issue 1, pp 1–15 | Cite as

Rotationally Invariant Rank 1 Convex Functions

  • M. Šilhavý

Abstract.

Let f be a function on the set M n xn of all n by n real matrices. If f is 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 f in terms of \tilde f .

Key words. Rank 1 convex functions, Rotational invariance. AMS Classification. Primary 49K20, Secondary 73C50. 

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Copyright information

© Springer-Verlag New York Inc. 2001

Authors and Affiliations

  • M. Šilhavý
    • 1
  1. 1.Mathematical Institute of the AV ČR, Žitná 25, 115 67 Prague 1, Czech Republic silhavy@math.cas.czCZ

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