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Orthogonal subspaces
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Notion
Orthogonal subspaces
Solve: Ax=bA\vec{x} = b when there is no solution.
Now, ATAx=ATb    N(ATA)=N(A)    rank(ATA)=rank(A)A^TAx = A^Tb \implies N(A^TA) = N(A) \implies rank(A^TA) = rank(A)
Thus, all rows of AA must be linearly independent.