Vector projection

Linear algebra · Formula · Not yet linked from a lesson

proj⁡ba=a⋅bb⋅bb\operatorname{proj}_{\mathbf{b}}\mathbf{a} = \frac{\mathbf{a} \cdot \mathbf{b}}{\mathbf{b} \cdot \mathbf{b}} \mathbf{b}

The shadow one vector casts on another: the part of a that lies along b, with the perpendicular part discarded. Least squares is this idea applied to a whole subspace at once.

Symbols

a\mathbf{a}
The vector being projected.
b\mathbf{b}
The direction it is projected onto.
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