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All about the \(\bot\) with its applications in the linear statistical models. (English) Zbl 1308.62145
Summary: For an \(n \times m\) real matrix \(\mathbf A\) the matrix \(\mathbf A^{\bot}\) is defined as a matrix spanning the orthocomplement of the column space of \(\mathbf A\), when the orthogonality is defined with respect to the standard inner product \(\langle \mathbf {x,y}\rangle = \mathbf{x'y}\). In this paper we collect together various properties of the \(\bot\) 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.

MSC:
62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
15B99 Special matrices
15A09 Theory of matrix inversion and generalized inverses
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