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Thatsme314 (talk | contribs) m →Blockwise formula: ce |
Thatsme314 (talk | contribs) m →Intuition: punctuation |
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From the figure, it is clear that the closest point from the vector <math>\mathbf{b}</math> onto the column space of <math>\mathbf{A}</math>, is <math>\mathbf{Ax}</math>, and is one where we can draw a line orthogonal to the column space of <math>\mathbf{A}</math>. A vector that is orthogonal to the column space of a matrix is in the nullspace of the matrix transpose, so
:<math>\mathbf{A}^\textsf{T}(\mathbf{b}-\mathbf{Ax}) = 0</math>.
From there, one rearranges, so
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