I am new to SVD so forgive me if the question is trivial. Following is my question. If I have two sets of linear equations,
Y1 = T1.X
Y2 = T2.X
where T1 and T2 are mxn rectangular matrices. Now let's assume that both equations have some redundant linear equations, with $\sigma_1$ and $\sigma_2$ (both less than m, n) non-zero singular values. If I construct a new sets of linear equations by taking sum of the above equations,
Y3 = T3.X
where Y3 = Y1+Y2 and T3 = T1+T2, how does the number of singular value change for the combined linear equation?
Also, assuming the transformation matrices T1 is less noisy than T2, how would the noise property of the new T3 matrix?