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This question is about equations where the unknown itself is a matrix such as Sylvester or Riccati equations. For systems of linear equations (where the unknown is a vector), use "linear-system".
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Linear least squares with selective parameter fitting
Suppose I have a linear model depending on 2 sets of parameters $a,b$
$$
z(t) = \sum_i a_i \Phi_i(t) + \sum_j b_j \Psi_j(t)
$$
Now suppose my data vector $z$ can be naturally divided into 2 sets: $x,y …