Solve matrix series equation

I have 7x2 matrix and 7x3 matrix that contains 2D coordinates and related 3D coordinates. I need to find the projection matrix( ) by using these 14 coordinates in below equation.

I gave a try using symbolic math toolbox. But I could not figure out a way to continue from this step.

syms x [2,1];
syms X [3,1];
syms r [2,3];
eq = x==r*X;

[Rik]

An exact solution might not be possible with numeric inputs. Did you try a numeric fitter? A right-division of one of the 2D sets by the 3D counterpart might give you a reasonable initial estimate for the projection matrix.

Answer 1

[David Goodmanson]

Hi Ramesh,

This is an overdetermined system, but if you define x as a 2x7 matrix of 2d coordinate values and X as a corresponding 3x7 matrix of 3d coordinate values, then

r = x/X

provides a least squares solution for r.