Let V be a finite-dimensional vector space over a field F, and let T:V → V be a linear transformation whose fifth power T³ is the identity. (a) Show that T is always diagonalisable if F is the field of complex numbers. (b) If F is the field of real numbers, show that T is only diagonalisable if it is equal to the identity.
Let V be a finite-dimensional vector space over a field F, and let T:V → V be a linear transformation whose fifth power T³ is the identity. (a) Show that T is always diagonalisable if F is the field of complex numbers. (b) If F is the field of real numbers, show that T is only diagonalisable if it is equal to the identity.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...
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