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Thatsme314 (talk | contribs) m →Intuition: punctuation |
Thatsme314 (talk | contribs) m →Intuition: punctuation |
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\Rightarrow && \mathbf{A}^\textsf{T}\mathbf{b} &= \mathbf{A}^\textsf{T}\mathbf{Ax} \\
\Rightarrow && \mathbf{x} &= \left(\mathbf{A}^\textsf{T}\mathbf{A}\right)^{-1}\mathbf{A}^\textsf{T}\mathbf{b}
\end{align}</math>.
Therefore, since <math>\mathbf{x}</math> is on the column space of <math>\mathbf{A}</math>, the projection matrix, which maps <math>\mathbf{b}</math> onto <math>\mathbf{x}</math> is just <math>\mathbf{A}</math>, or <math>\mathbf{A}\left(\mathbf{A}^\textsf{T}\mathbf{A}\right)^{-1}\mathbf{A}^\textsf{T}</math>.
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