Multi dimensional vector operation

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MarshallSc
MarshallSc on 14 Nov 2021
Commented: Matt J on 15 Nov 2021
Can someone please help me with figuring out the code for the operation below:
I have two sets of matrices, for example:
r_x=rand(3,3);r_y=rand(3,3);r_z=rand(3,3);
h_x=rand(3,3);h_y=rand(3,3);h_z=rand(3,3);
That is shown as, for x for example:
What I want to do is to take each component of the matrices in the 3 dimensions and form a column vector such that, for example for component (1,1):
r_11=[r_x(1,1);r_y(1,1);r_z(1,1)]; h_11=[h_x(1,1);h_y(1,1);h_z(1,1)]
And solve three sets of simultaneous equations:
Which essentially do this calculation:
I want to solve for the L matrix (r and h are known). I'd appreciate it if someone can please help me. Thank you.
  2 Comments
MarshallSc
MarshallSc on 15 Nov 2021
Yes, they are quadratic. My actual values are in complex conjugate format so it is not a problem if they're not real values.

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Accepted Answer

Matt J
Matt J on 14 Nov 2021
Edited: Matt J on 14 Nov 2021
L_squared=([hx(:),hy(:),hz(:)]\[rx(:),ry(:),rz(:)]).';
  2 Comments
Matt J
Matt J on 15 Nov 2021
For each component of H or R in 3D, I need to have the 3*3 matrix for each point.
You can't derive a 3x3 matrix L from two 3x1 vectors. That gives you only 3 equations for 9 unknowns.

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