All about the ⊥ with its applications in the linear statistical models

Abstract

For an n x m real matrix A the matrix A⊥ is defined as a matrix spanning the orthocomplement of the column space of A, when the orthogonality is defined with respect to the standard inner product ⟨x, y⟩ = x'y. In this paper we collect together various properties of the ⊥ operation and its applications in linear statistical models. Results covering the more general inner products are also considered. We also provide a rather extensive list of references

Keywords

• Best linear unbiased estimator
• Column space
• Generalized inverse
• Linear statistical model
• Orthocomplement
• Orthogonal projector