The germ of an algebraic variety (X,0) is naturally equipped with two different metrics: the outer metrics which is the restriction of the Euclidean metrics and the inner metrics which is defined using lengths of paths in X. The bilipschitz equivalence class of these metrics is an intrinsic property of the variety and do not depend of the choice of embeddings. If the inner metric is bilipschitz equivalent to the outer metric, we say that (X,0) is Lipschitz normally embedded. In this talk we prove Lipschitz normally embeddedness of some algebraic subsets of the space of matrices. Let X be a subset of the space of matrices, then let X(r) be the set of matrices in X of rank r, and X(
Kontakt: Jørgen Ellegaard Andersen
Revideret: 25.05.2023
