Determinantal variety and normal embedding

K. Katz; M. Katz; D. Kerner; Y. Liokumovich

doi:10.1142/S1793525318500073

Determinantal variety and normal embedding

K. Katz, M. Katz, D. Kerner, Y. Liokumovich

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The space GLn+ of matrices of positive determinant inherits an extrinsic metric space structure from ân2. On the other hand, taking the infimum of the lengths of all paths connecting a pair of points in GLn+ gives an intrinsic metric. We prove bi-Lipschitz equivalence between intrinsic and extrinsic metrics on GLn+, exploiting the conical structure of the stratification of the space of n × n matrices by rank.

Original language	English
Pages (from-to)	27-34
Number of pages	8
Journal	Journal of Topology and Analysis
Volume	10
Issue number	1
DOIs	https://doi.org/10.1142/S1793525318500073
State	Published - 1 Mar 2018

Keywords

Determinantal variety
bi-Lipschitz equivalence
conical stratification
intrinsic metric

ASJC Scopus subject areas

Analysis
Geometry and Topology

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10.1142/S1793525318500073

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abstract = "The space GLn+ of matrices of positive determinant inherits an extrinsic metric space structure from {\^a}n2. On the other hand, taking the infimum of the lengths of all paths connecting a pair of points in GLn+ gives an intrinsic metric. We prove bi-Lipschitz equivalence between intrinsic and extrinsic metrics on GLn+, exploiting the conical structure of the stratification of the space of n × n matrices by rank.",

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AU - Kerner, D.

AU - Liokumovich, Y.

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N2 - The space GLn+ of matrices of positive determinant inherits an extrinsic metric space structure from ân2. On the other hand, taking the infimum of the lengths of all paths connecting a pair of points in GLn+ gives an intrinsic metric. We prove bi-Lipschitz equivalence between intrinsic and extrinsic metrics on GLn+, exploiting the conical structure of the stratification of the space of n × n matrices by rank.

AB - The space GLn+ of matrices of positive determinant inherits an extrinsic metric space structure from ân2. On the other hand, taking the infimum of the lengths of all paths connecting a pair of points in GLn+ gives an intrinsic metric. We prove bi-Lipschitz equivalence between intrinsic and extrinsic metrics on GLn+, exploiting the conical structure of the stratification of the space of n × n matrices by rank.

KW - Determinantal variety

KW - bi-Lipschitz equivalence

KW - conical stratification

KW - intrinsic metric

UR - https://www.scopus.com/pages/publications/85009944139

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DO - 10.1142/S1793525318500073

M3 - Article

AN - SCOPUS:85009944139

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JF - Journal of Topology and Analysis

IS - 1

ER -

Determinantal variety and normal embedding

Abstract

Keywords

ASJC Scopus subject areas

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