If the spin operators for spin $1/2$ can be represented in matrix form using the Pauli Matrices, e.g $S_x = \frac{1}{2}\hbar \sigma_x = \frac{1}{2}\hbar \begin{bmatrix}0&1\\1&0\end{bmatrix}$, What is the physical meaning of the components of a spinor in this matrix representation?
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