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Question 3. Let V be a finite-dimensional complex vector space, and let f: VV be a linear map such that dim img f = 1. Prove that f is diagonalizable if and only if img fnker f = 0.

Question 3. Let V be a finite-dimensional complex vector space, and let f: VV be a linear map such that dim img f = 1. Prove that f is diagonalizable if and only if img fnker f = 0.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.CR: Review Exercises
Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...
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Question 3. Let V be a finite-dimensional complex vector space, and let f: VV be a linear map such that dim img f = 1. Prove that f is diagonalizable if and only if img fnker f = 0.
Transcribed Image Text:Question 3. Let V be a finite-dimensional complex vector space, and let f: VV be a linear map such that dim img f = 1. Prove that f is diagonalizable if and only if img fnker f = 0.
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