I know that a real matrix can have real and complex eigenvalues/eigenvectors, but what if we start with the condition that we have a real matrix with only real eigenvalues, is it possible for such a matrix to have complex eigenvectors?

I know that a real matrix can have real and complex eigenvalues/eigenvectors, but what if we start with the condition that we have a real matrix with only real eigenvalues, is it possible for such a matrix to have complex eigenvectors?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 79E

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I know that a real matrix can have real and complex eigenvalues/eigenvectors, but what if we start with the condition that we have a real matrix with only real eigenvalues, is it possible for such a matrix to have complex eigenvectors?

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