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double summation as a matrix

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  • 04-08-2015 2:27pm
    #1
    riffmongous
    Moderators, Society & Culture Moderators Posts: 12,709 Mod ✭✭✭✭


    Hi all, I am having trouble figuring out how to rewrite an equation, I am sure it's not too complicted but I just don't see it and it's starting to wreck my head and I am not very good with matrices in the first place so I thought I would ask for some assistance

    So first I had an equation

    6034073
    with i=5 and j =2

    Now to solve for Sj I have to use Singular Value Decomposition according to the paper it is described in, so I want it in the form Gm = d, with Mij as G, Sj as m and Ci as d, then I can invert it to m =G-1d to solve for Sj.

    So I wrote it all out explicitely and realised that if I write Ci as a 5x1 matrix and Mij as a 5x2 (including the delta z terms) and Sj as a 2x1 it is correct.

    The problem for me is that this equation is alone not sufficient and the following advanced form has to be solved as well
    357364.png

    but the second summation sign has got me confused and I cant wrap my head around it. Any advice or similar examples showing how to write this equation in matrix form would be appreciated!


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