  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.
