2. Let n>1 and let T: M₁(k) →→→ M₁(k) be the linear map defined by - T(A) = A + A¹ For k= R, C, F₂ determine the minimal polynomial of T (justify your answer) and in each case state whether T is diagonalisable. What are the eigenvalues of T? (Hint. Start by looking at T2...) Suppose k R. Find the characteristic polynomial chr. = (you may use without proof that the dimension of the space of symmetric matrices is n(n+1) and that of antisymmetric matrices is n(n-1)) 2 2

2. Let n>1 and let T: M₁(k) →→→ M₁(k) be the linear map defined by - T(A) = A + A¹ For k= R, C, F₂ determine the minimal polynomial of T (justify your answer) and in each case state whether T is diagonalisable. What are the eigenvalues of T? (Hint. Start by looking at T2...) Suppose k R. Find the characteristic polynomial chr. = (you may use without proof that the dimension of the space of symmetric matrices is n(n+1) and that of antisymmetric matrices is n(n-1)) 2 2

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices

Problem 29EQ

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