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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.

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)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
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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.
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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