Determinantal variety and normal embedding

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

doi:https://doi.org/10.1142/S1793525318500073

Determinantal variety and normal embedding

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

Ben-Gurion University of the Negev, Bar-Ilan University

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

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	American 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

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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Cite this

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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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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

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JO - Journal of Topology and Analysis

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IS - 1

ER -

Determinantal variety and normal embedding

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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