Quotient of subspace theorem
id:
quotient-of-subspace-theorem-244-8401444
title:
Quotient of subspace theorem
text:
In mathematics, the quotient of subspace theorem is an important property of finite-dimensional normed spaces, discovered by Vitali Milman. Let (X, ||·||) be an N-dimensional normed space. There exist subspaces Z ⊂ Y ⊂ X such that the following holds: The quotient space E = Y / Z is of dimension dim E ≥ c N, where c > 0 is a universal constant.
The induced norm || · || on E, defined by is uniformly isomorphic to Euclidean. That is, there exists a positive quadratic form ("Euclidean structure") Q
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original url:
https://en.wikipedia.org/wiki/Quotient_of_subspace_theorem
date created:
date modified:
2023-04-05T00:52:36Z
main entity:
{"identifier":"Q7272898","url":"https://www.wikidata.org/entity/Q7272898"}
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