Orthogonal projections
General · Mathematics
Study notes
Q: Project (3,4) onto u = (1,1). What is the closest point on span(u)? proj = ⟨(3,4),(1,1)⟩/⟨(1,1),(1,1)⟩(1,1) = (7/2)(1,1) = (3.5,3.5). Closest point on line y = x: (3.5,3.5)! Error: (3,4)-(3.5,3.5) = (-0.5,0.5) ⊥ u ✓! (Orthogonal error - best approximation!)