Vector space of C4\mathbb{C}^4 and its basis, the Pauli matrices

How do I write an arbitrary 2×2 matrix as a linear combination of the three Pauli Matrices and the 2×2 unit matrix?

Any example for the same might help ?


A slow construction would go…



(0100)= ...

(abcd)=a212+a2σ3+ ... (other combintations of the four matrices)

Source : Link , Question Author : chakra , Answer Author : Nikolaj-K

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