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I was wondering if the pseudoinverse can be considered a change of basis?

If an m x n matrix with m < n and rank m and you wish to solve the system Ax = b, the solution would hold an infinite number of solutions; hence you form the pseudoinverse by A^T(A*A^T)^-1 and solve for x to get the minimum norm solution. And since A was the original basis the pseudoinverse must be a new basis...? Or am I getting it all wrong?

Best regards,

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# Pseudoinverse - change of basis?

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