Log of 2x2 Matrix: Solving e^A= Ʃ (A^k)/k!

[jhendren]

Homework Statement

log of 2x2 matrix [4 3]
[3 4]

Homework Equations

e^X= A X= log A

The Attempt at a Solution

e^A= Ʃ (A^k)/k!

then what to do?

 

[Mark44]

Homework Statement

log of 2x2 matrix [4 3]
[3 4]

Homework Equations

e^X= A X= log A

The Attempt at a Solution

e^A= Ʃ (A^k)/k!

then what to do?

I'm not sure that what you've done will be much help. Have you learned matrix diagonalization yet? If so, your matrix is diagonalizable. See http://en.wikipedia.org/wiki/Logarithm_of_a_matrix, especially the section titled "Calculating the logarithm of a diagonalizable matrix".

 

[Borek]

https://www.physicsforums.com/showthread.php?t=641328