. 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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4725b67c-7cdd-4a39-ac18-c5ec8e35aaaa%2F72c3f027-160f-4f8f-9595-5a3ceaffcf71%2Fr088bk_processed.jpeg&w=3840&q=75)
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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