12. Let V be an inner product space, Vo be a subspace of V with dim(Vo) = k. Let {u1, ., uk} be an orthonormal basis of Vo. For xo E Vo, let xo = E;=1 < x,uj > uj. Prove that ||r – xo|| < ||x – u||, V u e Vo.
12. Let V be an inner product space, Vo be a subspace of V with dim(Vo) = k. Let {u1, ., uk} be an orthonormal basis of Vo. For xo E Vo, let xo = E;=1 < x,uj > uj. Prove that ||r – xo|| < ||x – u||, V u e Vo.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Plz solve 12
Transcribed Image Text:12. Let V be an inner product space, Vo be a subspace of V with dim(Vo) = k. Let
{u1, .., uk} be an orthonormal basis of Vo. For xo E Vo, let xo = E;=1 < x, uj > uj.
Prove that
||a – xo|| < || -
u|l, V u e Vo.
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