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The factor of 4 corresponds to the (nearly) four times greater population difference for compared to 13 C, which is a direct result of the (nearly) four times larger magnetogyric ratio of 1H. Note that the equilibrium state for this two-spin system is aeq = Iz + Sz, so that the sum of the two matrices above equals the matrix aeq.

In-phase single-quantum coherence (SQC) is represented by nonzero values for the matrix elements that correspond to the single-quantum transitions. For example, I spin (1H) SQC corresponds to a superposition of the aIaS and /aS states (row 1 and column 3), and the aI/S and //S states (row 2 and column 4). Real numbers are used for magnetization on the x' axis, and imaginary numbers are used for magnetization on the y' axis. Notice that the "downward" transition /aS ^ aIaS has a matrix element that is the complex conjugate of the "upward" transition aIaS ^ /IaS.

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