MT 김신휘 Computation of e^A using Jordan Canonical Form


MT Page 334 Problem 9.4

(2) Computation of the exponential matrix  of .

(Citation : Jin Ho Kwak and Sungpyo Hong, 1997, Linear Algebra, 334p)

 

Sol)

Let  be a Jordan form of  such that .

.

Also, when ,

.

 

 
A = matrix([[2,1,0,0],[0,2,1,0],[0,0,2,0],[0,0,0,1]])
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A = matrix([[2,1,0,0],[0,2,1,0],[0,0,2,0],[0,0,0,1]])
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[J,Q] = A.jordan_form(transformation=True)
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show(J)
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show(Q)
 
 



이제 sage를 이용해서 를 구하자.

 
EJ = matrix([[e,0,0,0],[0,e^2,e^2,e^2/2],[0,0,e^2,e^2],[0,0,0,e^2]])
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EJ = matrix([[e,0,0,0],[0,e^2,e^2,e^2/2],[0,0,e^2,e^2],[0,0,0,e^2]])
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EA = Q*EJ*Q^-1
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show(EA)
 
 



(Citation : Jin Ho Kwak and Sungpyo Hong, 1997, Linear Algebra, 334-335p)

Note

 -

 - 를 sage로 직접 구하는 것은 워크시트에서는 되지 않지만 공개를 한 문서에서는 가능하다.

 
e^A
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e^A
 
 



Reference

Jin Ho Kwak and Sungpyo Hong, 1997, Linear Algebra, 334-335p

SKKU Matrix Theory Contents

 
 
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