Let A be an n xna diagonalizable matrix. Prove that the matrix exponential satisfies det(e^) = e!r(4) (Hint: Use the representation of e^ in the previous problem and the properties of the PDP = Pe" P I determinant.) e1 e'

Let A be an n xna diagonalizable matrix. Prove that the matrix exponential satisfies det(e^) = e!r(4) (Hint: Use the representation of e^ in the previous problem and the properties of the PDP = Pe" P I determinant.) e1 e'

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.4: Orthogonal Diagonalization Of Symmetric Matrices

Problem 27EQ

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Question

Let A be an n xna diagonalizable matrix. Prove that the matrix exponential
satisfies
det(e^) = e!r(4)
(Hint: Use the representation of e^ in the previous problem and the properties of the
PDP = Pe" P I
determinant.)
e1 e'

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