Let V be finite-dimensional and let TE L(V). Prove or give a counterexample: If there exists an orthonormal basis €₁,e2,..., en of V such that |Tej|| = ||T*e;|| for each j, then T is normal.
Let V be finite-dimensional and let TE L(V). Prove or give a counterexample: If there exists an orthonormal basis €₁,e2,..., en of V such that |Tej|| = ||T*e;|| for each j, then T is normal.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 22EQ
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![or give a
Let V be finite-dimensional and let Te L(V). Prove
counterexample: If there exists an orthonormal basis e₁,e2,..., en of V such that
||Tej|| = ||T*e;|| for each j, then T is normal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0eb2c190-8d67-4c62-8b1d-a24b1a46a697%2F45453105-a198-4d59-b321-431ea0cbe0c0%2F07p26z7_processed.png&w=3840&q=75)
Transcribed Image Text:or give a
Let V be finite-dimensional and let Te L(V). Prove
counterexample: If there exists an orthonormal basis e₁,e2,..., en of V such that
||Tej|| = ||T*e;|| for each j, then T is normal.
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