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B = PAP^{T}\ ,  \end{equation}  where \(P\) is the orthogonal matrix that transforms any vector from  the basis $\{\psi_i\}$ to $\{\phi_i\}$. In Note that in  general, \(B\) is not a sparse matrix. If we regard \(A\) and \(B\) as \(N^2\)-element \emph{vectors}  formed by stacking the columns of the matrices, we can note that the change-of-basis