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 Tensor power series andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 05/14/2008, 06:18 AM At first, I thought you wouldn't need the factorials you usually need in normal power series, because all the coefficients in F' and F'' were less than the factorial, but then I realized that there were multiple coefficients in each tensor. So taking the logistic map as an example again: $ \left[\begin{tabular}{cc} [0\ 0] & [1\ 0] \\ [1\ 0] & [0\ 0] \\ \end{tabular}\right] \left[\begin{tabular}{c} z \\ r \end{tabular}\right]^{\otimes 2} = \left[\begin{tabular}{c} zr + rz \\ 0 \end{tabular}\right] = \left[\begin{tabular}{c} 2rz \\ 0 \end{tabular}\right]$ so $ \frac{1}{2!} \left[\begin{tabular}{cc} [0\ 0] & [1\ 0] \\ [1\ 0] & [0\ 0] \\ \end{tabular}\right] \left[\begin{tabular}{c} z \\ r \end{tabular}\right]^{\otimes 2} = \left[\begin{tabular}{c} rz \\ 0 \end{tabular}\right]$ as it should, and doing the same thing for the third term: $ \frac{1}{3!} \left[\begin{tabular}{cc} \left[\begin{tabular}{cc} 0 & 0 \\ -2 & 0 \end{tabular}\right] & \left[\begin{tabular}{cc} -2 & 0 \\ 0 & 0 \end{tabular}\right] \\ \left[\begin{tabular}{cc} -2 & 0 \\ 0 & 0 \end{tabular}\right] & \left[\begin{tabular}{cc} 0 & 0 \\ 0 & 0 \end{tabular}\right] \\ \end{tabular}\right] \left[\begin{tabular}{c} z \\ r \end{tabular}\right]^{\otimes 3} = \frac{1}{3!}\left[\begin{tabular}{c} -2z^2r -2zrz -2rz^2 \\ 0 \end{tabular}\right] = \left[\begin{tabular}{c} -rz^2 \\ 0 \end{tabular}\right]$ as it should. Andrew Robbins « Next Oldest | Next Newest »

 Messages In This Thread Tensor power series - by andydude - 05/13/2008, 07:58 AM RE: Tensor power series - by andydude - 05/13/2008, 07:59 AM RE: Tensor power series - by andydude - 05/13/2008, 08:11 AM RE: Tensor power series - by andydude - 05/14/2008, 06:18 AM RE: Tensor power series - by Gottfried - 05/20/2008, 08:39 PM RE: Tensor power series - by andydude - 05/22/2008, 12:58 AM RE: Tensor power series - by andydude - 05/22/2008, 04:11 AM RE: Tensor power series - by andydude - 05/22/2008, 04:36 AM RE: Tensor power series - by bo198214 - 05/24/2008, 10:10 AM RE: Tensor power series - by andydude - 06/04/2008, 08:08 AM

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