Gram-Schmidt orthogonalisation
General · Mathematics
Study notes
Q: Apply Gram-Schmidt to (1,1,0), (1,0,1), (0,0,1) in ℝ³. u₁ = (1,1,0). u₂ = (1,0,1) - ⟨(1,0,1),u₁⟩/⟨u₁,u₁⟩u₁ = (1,0,1) - (1/2)(1,1,0) = (1/2,-1/2,1). u₃ = (0,0,1) - proj: compute: (0,0,1)·u₁ = 0; ·u₂: (1)/(3/2) = 2/3. u₃ = (0,0,1)-(2/3)(1/2,-1/2,1) = (-1/3,1/3,1/3). Orthogonal ✓!