Determinantal variety and normal embedding
Katz, Karin U. · Katz, Mikhail G. · Kerner, Dmitry · Liokumovich, Yevgeny
Original · EN
The space of matrices of positive determinant GL+ₙ inherits an extrinsic metric space structure from Rⁿ². 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.
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