Determinantal variety and normal embedding

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

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish
Pages (from-to)27-34
Number of pages8
JournalJournal of Topology and Analysis
Issue number1
StatePublished - 1 Mar 2018


  • Determinantal variety
  • bi-Lipschitz equivalence
  • conical stratification
  • intrinsic metric

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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