defined by Let n ≥2. Consider the reversing operator R:R" R(a1, a2,,an-1, an) = (an, an-1,..., a2, a1). → Rn We denote by E₁ and E-1 the eigenspaces of eigenvalues λ = 1 and λ = −1, respec- tively. (1) If n is even, find a basis of E₁ and a basis of E-1, and determine whether or not R is diagonalizable. (2) If n is odd, find a basis of E₁ and a basis of E-1, and determine whether or not R is diagonalizable.

defined by Let n ≥2. Consider the reversing operator R:R" R(a1, a2,,an-1, an) = (an, an-1,..., a2, a1). → Rn We denote by E₁ and E-1 the eigenspaces of eigenvalues λ = 1 and λ = −1, respec- tively. (1) If n is even, find a basis of E₁ and a basis of E-1, and determine whether or not R is diagonalizable. (2) If n is odd, find a basis of E₁ and a basis of E-1, and determine whether or not R is diagonalizable.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 11AEXP

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