If x₁ is orthonormal set i=1,2,...,n in a Hilbert space and xEH then |x-₁=₁(x,x₁)|x₁||² = (x,x) - Σ₁(x,x₁)|² Option 1 ≤||x||² i=1 ||(x,x₁)x; ||² n = |x||² - 11(x,x₁)x,11²2 Option 3 i=1 ≤||x||²₁||x||²2 ||x; ||²
If x₁ is orthonormal set i=1,2,...,n in a Hilbert space and xEH then |x-₁=₁(x,x₁)|x₁||² = (x,x) - Σ₁(x,x₁)|² Option 1 ≤||x||² i=1 ||(x,x₁)x; ||² n = |x||² - 11(x,x₁)x,11²2 Option 3 i=1 ≤||x||²₁||x||²2 ||x; ||²
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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Transcribed Image Text:/e/1FAIpQLSeh-VXHk0Cg791RQsReSpIMDQXIDDskMHz19h3n-11mOaL6iA/F
If x; is orthonormal set i=1,2,...,n in a Hilbert space and
xEH then ||x - Σ₁₁(x, x₁)|x₁|1²
= (x,x) – Σ,{x,x;}|2
Option 1
≤ ||1x||² - ||(x,x₁)x₁||²
i=1
n
=
= ||x|1|² - Σ||(x,x;>x;||²2
Option 3
i=1
≤||x||²₁||x||² ||x; ||²2
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