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## Main Question or Discussion Point

I went through the derivation for the central equation

$$(\lambda_k - \epsilon)C_k + \Sigma_G U_G C_{k-G} = 0$$

and everywhere I look everybody just says this is a NxN matrix. I don't see how this is true. Isn't this just a one line equation with summation across all reciprocal lattice? I don't understand why at one value of k we get NxN matrix. Any help is greatly appreciated!

$$(\lambda_k - \epsilon)C_k + \Sigma_G U_G C_{k-G} = 0$$

and everywhere I look everybody just says this is a NxN matrix. I don't see how this is true. Isn't this just a one line equation with summation across all reciprocal lattice? I don't understand why at one value of k we get NxN matrix. Any help is greatly appreciated!