What is it about?
The Cosserat microrotation problem amounts to minimizing a matrix-variate energy function, that is a squared Frobenius norm, for each in the space of matrices with positive determinant. The group of these matrices is the natural group to describe deformations of physical materials. In the very recent solution to this problem by Borisov, Fischle, and Neff, it is clearly seen that multiple singular values cause certain problems; yet this situation is far from pathological from a physical perspective, because it represents symmetries in the model of the physical material. We suggest to split of the polar factor in this problem by way of polar decomposition, and to use horospherical coordinates on the eigenvalues of the polar factor (which are the square roots of the singular values mentioned above).
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Why is it important?
In many areas of mathematics, including statistics, the problem of coinciding eigenvalues occurs. The solution to use horospherical coordinates is, however, to our knowledge new.
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This page is a summary of: Horospherical coordinates for optimal Cosserat microrotations, Mathematical Methods in the Applied Sciences, April 2018, Wiley,
DOI: 10.1002/mma.4897.
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