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= {ua}. An orthonormal set {ua} in a Hilbert space ♬ is said to be an honormal basis for H if it is maximal in the sense that if {u} is tained in some orthonormal subset E of H, then, in fact, E Let H be a Hilbert space and H ‡ {0}. Then H does contain honormal sets. For example, if x is a nonzero element of H, then ||~||} is surely an orthonormal set in H. To see that H contains

= {ua}. An orthonormal set {ua} in a Hilbert space ♬ is said to be an honormal basis for H if it is maximal in the sense that if {u} is tained in some orthonormal subset E of H, then, in fact, E Let H be a Hilbert space and H ‡ {0}. Then H does contain honormal sets. For example, if x is a nonzero element of H, then ||~||} is surely an orthonormal set in H. To see that H contains

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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An orthonormal set {ua} in a Hilbert space H is said to be an orthonormal basis for H if it is maximal in the sense that if {u} is contained in some orthonormal subset E of H, then, in fact, E = {u}. Let H be a Hilbert space and H ‡ {0}. Then H does contain orthonormal sets. For example, if x is a nonzero element of H, then {x/||||} is surely an orthonormal set in H. To see that H contains an orthonormal basis, and in fact, every orthonormal set E in H can Request Explain has
Transcribed Image Text:An orthonormal set {ua} in a Hilbert space H is said to be an orthonormal basis for H if it is maximal in the sense that if {u} is contained in some orthonormal subset E of H, then, in fact, E = {u}. Let H be a Hilbert space and H ‡ {0}. Then H does contain orthonormal sets. For example, if x is a nonzero element of H, then {x/||||} is surely an orthonormal set in H. To see that H contains an orthonormal basis, and in fact, every orthonormal set E in H can Request Explain has
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