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 Complement How to Examples Exercise How to: An orthogonal complement of a subspace V of Rn is the collection of all the vectors which are orthogonal to V. So, if we have a basis for V, say, v1, v2, ... , vM, then to calculate the orthogonal complement of V, we need to find all the vectors x, such that:      dot(v1, x) == 0      dot(v2, x) == 0      ...      dot(vM, x) == 0      Examples: Exercise: