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Suppose a 2x2 matrix X (not neccessarily Hermitian, nor unitary) is written as

[tex]X=a_0+\sigma \cdot a [/tex],

where a_0 and a_k (k=1,2,3) are numbers.

a. How are a_0 and a_k related to tr(X) and tr([tex]\sigma_k X[/tex] )

b. Obtain a_0 and a_k in terms of the matrix elements [tex]X_{ij}[/tex]

Now I have no idea what the matrix X is supposed to look like. Nor can I even figure out how a 2x2 matrix could be written like that. I remember seeing someone ask something about the same excercise here but I couldn't find that thread via search. I can't really present any work here since I don't know what the matrix is supposed to look like but could someone help me get started with this anyway?