Problem 1. Let E be a real vector space, F be a closed subspace of E, and a € E\F. Set d(a, F) inf{||a - r||; x € F}. 1. Show that if F ha a finite dimension then there exists zo € F such that d(x, F) = ||x-xo||.
Problem 1. Let E be a real vector space, F be a closed subspace of E, and a € E\F. Set d(a, F) inf{||a - r||; x € F}. 1. Show that if F ha a finite dimension then there exists zo € F such that d(x, F) = ||x-xo||.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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