All about the perpendicular to with its applications in the linear statistical models

作者：Markiewicz Augustyn; Puntanen Simo^*

来源：Open Mathematics, 2015, 13(1): 33-50.

DOI：10.1515/math-2015-0005

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

For an n x m real matrix A the matrix A(perpendicular to) 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 perpendicular to 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.

• 出版日期2015-1