2. Let (ei)ier and (fi) jer be the orthonormal bases for the Hilbert spaces X and Y respec- tively. If for each i Є I, set T(ei) = fi, show that T can be extended to a unitary operator from X onto Y.
2. Let (ei)ier and (fi) jer be the orthonormal bases for the Hilbert spaces X and Y respec- tively. If for each i Є I, set T(ei) = fi, show that T can be extended to a unitary operator from X onto Y.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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![2. Let (ei)ier and (fi) jer be the orthonormal bases for the Hilbert spaces X and Y respec-
tively. If for each i Є I, set T(ei) = fi, show that T can be extended to a unitary
operator from X onto Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Facf7d07c-fe42-4abc-9ecb-230578907529%2Feb4f2a66-4130-46aa-bff6-49922ba2e9c0%2Fdkj3cad_processed.png&w=3840&q=75)
Transcribed Image Text:2. Let (ei)ier and (fi) jer be the orthonormal bases for the Hilbert spaces X and Y respec-
tively. If for each i Є I, set T(ei) = fi, show that T can be extended to a unitary
operator from X onto Y.
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