Determinantal variety and normal embedding

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 me...

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Bibliographic Details
Published in:arXiv.org 2016-09
Main Authors: Katz, Karin U, Katz, Mikhail G, Kerner, Dmitry, Liokumovich, Yevgeny
Format: Article
Language:English
Subjects:
Conical bodies
Infimum
Metric space
Stratification
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1602.01227