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These matrices are the Pauli matrices \begin{align} A_1 & = \left[\begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}\right] \\ A_2 & = \left[\begin{array}{cc} 0 & -i \\ i & 0 \end{array}\right] \\ A_3 & = \left[\begin{array}{cc} 1 & 0 \\ 0 & -1 \end{array}\right] \\ \end{align} Consider an arbitrary $2\times 2$ matrix $M$. Then, what are the matrix exponentials $\exp(MA_i)$ for $i=1,2,3$?

Thanks!

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What is the $M$ in $\exp(MA_i)$ (or exp(MAi))? – Lord Soth Apr 17 '13 at 17:24
    
M is 2x2 matrix. Thanks – xxxx Apr 17 '13 at 17:30
    
I mean e^(M*Ai) where i=1,2,3 – xxxx Apr 17 '13 at 17:30
    
So $M$ can be an arbitrary $2\times 2$ matrix, or is it positive definite, etc? – Lord Soth Apr 17 '13 at 17:33
    
Let's assume that is arbitrary matrix – xxxx Apr 17 '13 at 17:41

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