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Each dipole has three vector components (<math>x</math>, <math>y</math>, <math>z</math>), so we can rearrange the unknown vector <math>\mathbf{P}</math> by grouping all x-components together, then y-components, then z-components:
:<math>
\mathbf{P} =
\begin{bmatrix}
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\mathbf{P}_y \\
\mathbf{P}_z
\end{bmatrix}
\in \mathbb{C}^{3N} \quad \text{where} \quad \mathbf{P}_x =
\begin{bmatrix}
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Similarly, the incident field can be grouped as:
:<math>▼
▲<math>
▲\mathbf{E}^{\mathrm{inc}} =
\begin{bmatrix}
\mathbf{E}_x^{\mathrm{inc}} \\
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\mathbf{E}_z^{\mathrm{inc}}
\end{bmatrix}
\in \mathbb{C}^{3N}
</math>
Because the system is linear, we can equivalently rewrite it in block matrix form, that describe how the <math>\beta</math>-component of polarization affects the <math>\alpha</math>-component of the resulting field:
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