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Determinantal variety and normal embedding (1602.01227v3)
Published 3 Feb 2016 in math.AG and math.DG
Abstract: The space of matrices of positive determinant GL+_n inherits an extrinsic metric space structure from R{n2}. 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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