Elementary projection operator

• Vector $\mathbf w$ defining linear functional $\mathbf w^{\scriptscriptstyle\mathsf{T}}$ (move this by dragging the head of the arrow)
• Vector $\mathbf z$ NOT in hyperplane $\operatorname{NS}(\mathbf w^{\scriptscriptstyle\mathsf{T}})$ (move this by dragging the head of the arrow)
• Projection operator is $P = \frac1{\mathbf w^{\scriptscriptstyle\mathsf{T}} \mathbf z} \mathbf z \mathbf w^{\scriptscriptstyle\mathsf{T}}$; projects to $\operatorname{span}(\mathbf z)$ along hyperplane $\operatorname{NS}(\mathbf w^{\scriptscriptstyle\mathsf{T}})$
• Input vector $\mathbf v$ (move this by dragging the head of the arrow)
• Output vector $P\mathbf v$ (automatically computed for your convenience)
• Bonus output vector $(I-P)\mathbf v$ (automatically computed for your convenience)

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