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MathGround

Gram-Schmidt 3D without normalization

  1. w⃗1=v⃗1\vec w_1=\vec v_1
  2. w⃗2=v⃗2−v⃗2⋅w⃗1w⃗1⋅w⃗1 w⃗1\vec w_2=\vec v_2-\dfrac{\vec v_2\cdot\vec w_1}{\vec w_1\cdot\vec w_1}\,\vec w_1
  3. w⃗3=v⃗3−v⃗3⋅w⃗1w⃗1⋅w⃗1 w⃗1−v⃗3⋅w⃗2w⃗2⋅w⃗2 w⃗2\vec w_3=\vec v_3-\dfrac{\vec v_3\cdot\vec w_1}{\vec w_1\cdot\vec w_1}\,\vec w_1-\dfrac{\vec v_3\cdot\vec w_2}{\vec w_2\cdot\vec w_2}\,\vec w_2
‖w₁‖,‖w₂‖,‖w₃‖ = — (≠ 1)w₁·w₂, w₁·w₃, w₂·w₃ = —