Abstract
This chapter discusses projection theorems and the Gauss–Markov theorem. Vectors x and y belonging to an inner product space are said to be orthogonal if (x | y) = 0. If x is orthogonal to y in an inner product space, then ∥x ± y∥2 = ∥x∥2 + ∥y∥2. If S is a subset of an inner product space X, then the set of all vectors in X orthogonal to every element of S is called the orthogonal complement of S. All vectors are supposed to be column vectors if not mentioned otherwise, and vectors and matrices are all defined over the field of real numbers.
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