How does one see the statistical aspects of the solution to a linear system?
Say, how does one see that a solution is unbiased and so on?
Given a linear system A*x = b, A is m-by-n. The solution x could be:
1. m > n, x = inv( A^T*A )*A^T*b 2. m = n, x = inv(A)*b 3. m < n, x = A^T*inv( A*A^T )*b
Nevertheless, it is heard that one can solve A*x = b from statistical perspective to get something like a linear unbiased estimator. Furthermore, one could analyze the solution in the case that the variances are either identical or different.
Could someone show how to understand this linear system from statistical aspect?