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 May 30th, 2019, 11:39 PM #1 Newbie   Joined: May 2019 From: london Posts: 1 Thanks: 0 tensor: outer product, representation, decomposition It is given a tensor: $T=\begin{pmatrix} 1\\ 1 \end{pmatrix}\circ \begin{pmatrix} 1\\ 1 \end{pmatrix}\circ\begin{pmatrix} 1\\ 1 \end{pmatrix}+\begin{pmatrix} -1\\ 1 \end{pmatrix}\circ\begin{pmatrix} 1\\ -1 \end{pmatrix}\circ\begin{pmatrix} -1\\ 1 \end{pmatrix}$ 1) Why is it possible to write the tensor T as: $T=\begin{pmatrix} 2 &0 \\ 0& 2 \end{pmatrix} and \begin{pmatrix} 0 &2 \\ 2& 0 \end{pmatrix}$ it is given in example that I can represent the tensor T as a sum of the outer product of vector triples and as 2 matrices. I have computed the outer product of the vector triples, but I can't get the same result. Can someone provide me detailed calculation? 2) T=[[ABC]] $A=\begin{pmatrix} 1 &-1 \\ 1& 1 \end{pmatrix}$ $B=\begin{pmatrix} 1 &1 \\ 1& -1 \end{pmatrix}$ $C=\begin{pmatrix} 1 &-1 \\ 1& 1 \end{pmatrix}$ **How to compute A, B, C?** Later on the p 35 (53), example 2. or on p 36(54) 2.2.1 the vectors a,b,c are given without an explanation of how he/she competed them. In §2.2.1 it is given that "we set...." and it is all. No explanation of how they find them. I have found examples in [Analysis of 2 × 2 × 2 Tensors], p 30 (48 in pdf file) example 1,6. In this example is given a calculation of a rank of T and these decompositions without explanation. Can someone help me to understand the example? : http://e-spacio.uned.es/fez/eserv.ph...=Documento.pdf Last edited by skipjack; May 31st, 2019 at 03:18 AM. Tags decomposition, outer, product, representation, tensor Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mona123 Abstract Algebra 0 May 3rd, 2018 12:32 AM guynamedluis Real Analysis 1 March 13th, 2012 11:10 AM pascal4542 Abstract Algebra 0 February 12th, 2010 10:30 AM otaniyul Linear Algebra 0 October 30th, 2009 06:40 PM dimper129 Linear Algebra 0 October 15th, 2009 02:09 AM

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