Rank invariance criterion and its application to the unified theory of least squares

DOI10.1016/0024-3795(90)90352-DzbMath0694.15003MaRDI QIDQ908988

Jerzy K. Baksalary, Thomas Mathew

Publication date: 1990

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

matrix productrankgeneralized inversestatisticstheory of least squares

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Theory of matrix inversion and generalized inverses (15A09) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (19)

A new approach to the concept of a strong unified-least-squares matrix ⋮ Some Further Remarks on the Linear Sufficiency in the Linear Model ⋮ Further results on invariance of the eigenvalues of matrix product involving generalized inverses ⋮ Comment on range invariance of matrix products ⋮ Note on the invariance properties of operator products involving generalized inverses ⋮ Rank formulae from the perspective of orthogonal projectors ⋮ Some notes on linear sufficiency ⋮ All about the \(\bot\) with its applications in the linear statistical models ⋮ Invariance properties of a triple matrix product involving generalized inverses ⋮ An invariance property of operator products related to the mixed-type reverse order laws ⋮ Equalities between OLSE, BLUE and BLUP in the linear model ⋮ Spectrum and trace invariance criterion and its statistical applications ⋮ A Useful Matrix Decomposition and Its Statistical Applications in Linear Regression ⋮ Left-star and right-star partial orderings ⋮ An invariance property related to the mixed-type reverse order laws ⋮ Effect of adding regressors on the equality of the BLUEs under two linear models ⋮ On the Wedderburn-Guttman theorem ⋮ More on maximal and minimal ranks of Schur complements with applications ⋮ Upper and lower bounds for ranks of matrix expressions using generalized inverses

Cites Work

• 1-2 inverses and the invariance of \(BA^+C\)
• Range invariance of certain matrix products
• Categorical information and the singular linear model
• Unified Least Squares Approach to Linear Estimation in a General Gauss–Markov Model
• When Does Rank(A+B)=Rank(A)+Rank(B)?
• Unified theory of least squares
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Rank invariance criterion and its application to the unified theory of least squares