How do you find the vector that minimizes $\|A\mathbf{x}-\mathbf{b}\|_2^2$ ?
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$\|A\mathbf{x}-\mathbf{b}\|^2 $
where $\left \| \cdot \right \|$ is the Euclidean norm. In matrix notation the solution, denoted by $\hat{x}$, is given by:
$\hat{x} = (A^{T}A)^{-1}A^{T}\mathbf{b}$
Carl
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