Matrix distribution into two vectors that build similiar matrix as a vector product
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Hello,
i want to split up a matrix into two vectors. If i build the vector product of those vectors a similiar matrix compared to the original one should emerge. This should be an optimization problem, but i don't know where to start.
Furthermore the solution should not be an iterative one.
Thank you guys a lot!
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Torsten
2022-10-26
But you already got the answer for the two vectors a and b and the resulting approximating matrix C:
[u s v] = svd(M);
n = 1; % initially
a = n*u(:,1);
b = (s(1,1)/n)*v(:,1);
C = a*b'
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Torsten
2022-10-26
It's the best reconstruction for M2D that you can get from two vectors. You can't expect a perfect equality (M2D = a*b') since rank(a*b') = 1 whereas rank(M2D) = 4 usually.
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