| dbp:proof
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- Let be the space of solutions to , then since at each Kaczmarz iteration, is a vector parallel to , the final solution is a linear sum of .
Now, is parallel to the kernel of , so it is perpendicular to every , so the final is perpendicular to , meaning it is the minimal-norm solution.
Let be the minimal-norm solution. If is not , then after one iteration through all rows of , it must have been orthogonally projected at least once, so that , where is the largest acute angle between the hyperplanes defined by . (en)
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