Utilidades

1. Produto escalar: [; \underline{u} \cdot \underline{v}=\displaystyle \sum_{i=1}^N u_i~v_i ;]
2. Square Length: [; |\underline{u}|^2=\underline{u} \cdot \underline{u}=\displaystyle \sum_{i=1}^N u_i^2 ;]
3. Normalização: [; \underline{e}=\frac{\underline{v}}{ \underline{v}} ;]
4. Projeção de [; \underline{u} ;] em [; \underline{v};]: [; \underline{u}_{\parallel}= \frac { \underline{u} \cdot \underline{v} }{ |\underline{v}|^2 } \underline{v} = (\underline{u} \cdot \underline{e}) \underline{e} ;]
5. Complemento Ortogonal: [; \underline{u}_{\perp}+\underline{u}_{\parallel} = \underline{u} ;] [; \underline{u}_{\perp}= \underline{u}-\underline{u}_{\parallel} = \underline{u}-(\underline{u} \cdot \underline{e}) \underline{e} ;] [; \underline{u}_{\parallel} \cdot \underline{u}_{\perp} = \underline{e} \cdot \underline{u}_{\perp} = \underline{v} \cdot \underline{u}_{\perp} =0 ;]