Question: Suppose a 2 x 2 matrix X (not necessarily Hermitian. nor unitary) is written as X = 0 + a, where 0 and

Suppose a 2 x 2 matrix X (not necessarily Hermitian. nor unitary) is written as X = α0 + σ ∙ a, where α0 and α1, 2, 3 are numbers.

a. How are α0 and αk (k = 1, 2, 3) related to tr (X) and tr (σk X)?

b. Obtain α0 and αk in terms of the matrix elements Xij.

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