A matrix M ?R2x2 is a linear transformation: R2 ? R2. Given a dataset {(xi, yi)}i=1N where xi, yi ? R2. We are going to fit a linear transformation y = Mx. (i) (2 pts) How many degrees of freedom does M have? How many samples are required to find M? (ii) (1 pt) Suppose we have a dataset {(xi, yi)}Ni=1 and want to fit y = Mx. Formulate the fitting problem into the form of a least squares problem: argminm?Am ? b?2 where m is some vector that has all the parameters of M.
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