Answered: map T:V→V to Problem 5: Prove that the… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section: Chapter Questions

Problem 3RQ

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result from problem 10 of homework 2:

v₁ + v₂+ ... + v_k is in W, then v_{i ∈}W for all i.

please show clear. thanks

Problem 5: Prove that the restriction of a diagonalizable linear map T : V → V to
any non-trivial T-invariant subspace of V is also diagonalizable. (Hint: If T: V → V
1
is diagonalizable, then V is a direct sum of the eigenspaces of T. Now use the result
from problem 10 of homework 2.)

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