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'

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.6: The Algebra Of Matrices

Problem 13E

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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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