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. If X is finite dimensional Hilbert space, then it has Orthonormal basis. 0. Let {x} be an Orthonormal sequence in a pre-Hilbert spaceX and let xe X. Show that

. If X is finite dimensional Hilbert space, then it has Orthonormal basis. 0. Let {x} be an Orthonormal sequence in a pre-Hilbert spaceX and let xe X. Show that

Advanced Engineering Mathematics
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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9. If X is finite dimensional Hilbert space, then it has Orthonormal basis. 10. Let {x} be an Orthonormal sequence in a pre-Hilbert space X and let xe X. Show that x=y LM, where y = £4,5, and M =[Full- 11. Show that In a finite dimensional normed space, each closed and bounded set is compact. 12. Let A be a subset of a Hilbert space X . Show that a.. A¹ = A¹ b.. A¹ = [4] c.. A is dense in X iff A² = {0} 13. Let X,Y are Hilbert space on a field F. Show that X,Y are Hilbert Isomorphic iff dim X = dim Y
Transcribed Image Text:9. If X is finite dimensional Hilbert space, then it has Orthonormal basis. 10. Let {x} be an Orthonormal sequence in a pre-Hilbert space X and let xe X. Show that x=y LM, where y = £4,5, and M =[Full- 11. Show that In a finite dimensional normed space, each closed and bounded set is compact. 12. Let A be a subset of a Hilbert space X . Show that a.. A¹ = A¹ b.. A¹ = [4] c.. A is dense in X iff A² = {0} 13. Let X,Y are Hilbert space on a field F. Show that X,Y are Hilbert Isomorphic iff dim X = dim Y
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