Projection on a lineVectors > Basics | Scalar product, Norms | Projection on a line | Orthogonalization | Hyperplanes | Linear functions | Application
DefinitionConsider the line in ![]() The projection of a given point ![]() This particular problem is part of a general class of optimization problems known as least-squares. It is also a special case of a Euclidean projection on a general set. Closed-form expressionAssuming that ![]() Thus, the optimal solution to the projection problem is ![]() and the expression for the projected vector is ![]() The scalar product In the case when ![]() Interpreting the scalar productWe can now interpret the scalar product between two non-zero vectors In general, the scalar product |