Answered: Let V be a finite dimensional vector…

Let V be a finite dimensional vector space with inner product 〈, 〉. Let T be a unitary operator on V . Let W be a T -invariant subspace of V . Prove that W ^⊥ is also T -invariant

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 43EQ

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Question

Let V be a finite dimensional vector space with inner product 〈, 〉. Let
T be a unitary operator on V . Let W be a T -invariant subspace of V .
Prove that W ^⊥ is also T -invariant.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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