• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 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

 Possibly Related Threads... Thread Author Replies Views Last Post Perhaps a new series for log^0.5(x) Gottfried 3 675 03/21/2020, 08:28 AM Last Post: Daniel A Notation Question (raising the highest value in pow-tower to a different power) Micah 8 3,753 02/18/2019, 10:34 PM Last Post: Micah Taylor series of i[x] Xorter 12 13,258 02/20/2018, 09:55 PM Last Post: Xorter Functional power Xorter 0 1,501 03/11/2017, 10:22 AM Last Post: Xorter 2 fixpoints related by power ? tommy1729 0 1,655 12/07/2016, 01:29 PM Last Post: tommy1729 Taylor series of cheta Xorter 13 14,327 08/28/2016, 08:52 PM Last Post: sheldonison Inverse power tower functions tommy1729 0 2,026 01/04/2016, 12:03 PM Last Post: tommy1729 Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 5,630 05/06/2014, 09:47 PM Last Post: tommy1729 [integral] How to integrate a fourier series ? tommy1729 1 2,777 05/04/2014, 03:19 PM Last Post: tommy1729 about power towers and base change tommy1729 7 9,030 05/04/2014, 08:30 AM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)