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Q1. Let A be a set contained in a given Hilbert space H. State the conditions for A to be orthonormal in H. Given that A be an orthonormal, x,,x,...x, A and ye H. Prove the following: 2 i. (x,x) SDF 21

Q1. Let A be a set contained in a given Hilbert space H. State the conditions for A to be orthonormal in H. Given that A be an orthonormal, x,,x,...x, A and ye H. Prove the following: 2 i. (x,x) SDF 21

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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QI. Let A be a set contained in a given Hilbert space H. State the conditions for A to be orthonormal in H. Given that A be an orthonormal, x,x,.x, e A and yeH. Prove the following:
Transcribed Image Text:QI. Let A be a set contained in a given Hilbert space H. State the conditions for A to be orthonormal in H. Given that A be an orthonormal, x,x,.x, e A and yeH. Prove the following:
ii. The set E - {xe A:(x,y) 0} is countable ii If ze H, then K*, )(*.=)s!=l»l
Transcribed Image Text:ii. The set E - {xe A:(x,y) 0} is countable ii If ze H, then K*, )(*.=)s!=l»l
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