Commit 0cd2885c by D'azevedo, Ed

### minor update

parent 4d408ae1
 ... ... @@ -249,18 +249,20 @@ block diagonal matrix of the form $\tV_k \otimes \tU_k$ (such as moving the center site from site $i$ to site $i+1$), then we may have the change of basis operation by evaluting $\mbox{pinv}(V_k \otimes U_k) * (\tV_k \otimes \tU_k)$ $\mbox{pinv}(\tV_k \otimes \tU_k) * (V_k \otimes U_k) * \mbox{vec}(D_k)$ where $\mbox{pinv}$ is the least-squares pseudo-inverse. % Since $V_k$ and $U_k$ have ortho-normal columns, then $\mbox{pinv}(V_k) = V_k'$ and $\mbox{pinv}(U_k) = U_k'$ and $\mbox{pinv}( V_k \otimes U_k) = V_k' \otimes U_k'$. Since $\tV_k$ and $\tU_k$ have ortho-normal columns, then $\mbox{pinv}(\tV_k) = \tV_k'$ and $\mbox{pinv}(\tU_k) = \tU_k'$ and $\mbox{pinv}( \tV_k \otimes \tU_k) = \tV_k' \otimes \tU_k'$. % Then $(V_k' \otimes U_k') * (\tV_k \otimes \tU_k)$ can be evaluated as $(V_k'*\tV_k) \otimes (U_k' * \tU_k)$. Then $(\tV_k' \otimes \tU_k') * (V_k \otimes U_k)* \mbox{vec}(D_k)$ can be evaluated as $(\tV_k'*V_k) \otimes (\tU_k' * U_k)* \mbox{vec}(D_k)$ or $(\tU_k' * U_k) * (D_k) * ( \tV_k' \otimes V_k')^t$. % Note that in general the rectangular matrices $V_k$ and $\tV_k$ Note that in general the rectangular matrices $V_k$, $\tV_k$, $U_k$, $\tU_k$ have in compatible shapes and one may assume the matrices are padded with zeros to be of the appropriate size. % ... ...
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