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arXiv · 1602.01227

Determinantal variety and normal embedding

Karin U. Katz·Mikhail G. Katz·Dmitry Kerner·Yevgeny Liokumovich
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Abstract

The space of matrices of positive determinant GL^+_n inherits an extrinsic metric space structure from R^{n^2}. On the other hand, taking the infimum of the lengths of all paths connecting two points in GL^+_n gives an intrinsic metric. We prove bilipschitz equivalence for intrinsic and extrinsic metrics on GL^+_n, exploiting the conical structure of the stratification of the space of n by n matrices by rank.

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Karin U. Katz, Mikhail G. Katz, Dmitry Kerner, Yevgeny Liokumovich. 2016-09-27. Determinantal variety and normal embedding. https://doi.org/10.1142/s1793525318500073

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