ORTHOGONALITY AND LEAST SQUARES

Orthogonal Vectors Norm Unit Vector Orthonormal Vectors Orthogonal Complement Orthogonal Projection Cauchy-Schwarz Inequality Angle Between Two Vectors Gram-Schmidt Process QR Factorialization Transpose Symmetric and Skew-symmetric Matrices Orthogonal Matrices Least Squares Solutions Matrix of an Orthogonal Projection

Orthogonal Projection How to Examples Exercise How to: An orthogonal projection of a vector x onto a subspace V, both in Rn, is a vector, denoted projVx, such that projVx is in V and x - projVx is in the orthogonal complement of V. To be able to simply find this vector, projVx, V must have an orthonormal basis, v1, v2, ... , vM. Once we have this basis, the calculation is easy:      projVx = dot(v1, x)*v1 + dot(v2, x)*v2 + ... + dot(vM, x)*vM      Examples: Exercise: