Determinantal variety and normal embedding

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.

8 pages. To appear in Journal of Topology and Analysis

References in corpus (3)

• Differential geometry via infinitesimal displacements
• Lipschitz Normal Embeddings and Determinantal Singularities
• Small oscillations of the pendulum, Euler's method, and adequality

Cited by in corpus (2)

• On Lipschitz Normally Embedded singularities
• Lipschitz Normal Embeddings in the Space of Matrices