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

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SUMMARY

The discussion focuses on calculating the logarithm of a 2x2 matrix, specifically the matrix [[4, 3], [3, 4]]. The key equation used is e^A = Σ (A^k)/k!, which relates the matrix exponential to its logarithm. A participant suggests that matrix diagonalization is essential for solving this problem, referencing the Wikipedia article on the logarithm of a matrix for further guidance. The matrix in question is confirmed to be diagonalizable, which simplifies the logarithm calculation process.

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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?
 
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jhendren said:

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".
 

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