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.
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 44EQ
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