Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

DOI10.1080/03081080500149040zbMath1083.15007OpenAlexW2061558094MaRDI QIDQ5693575

George P. H. Styan, Yongge Tian

Publication date: 26 September 2005

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

Full work available at URL: https://doi.org/10.1080/03081080500149040

zbMATH Keywords

Kronecker productWishart distributionchi-squared distributionidempotent matrixrank additivityrank formulas for partitioned matricesmatrix quadratic formrank equalitiesquadratic forms in normal variablesmatrix version of Chochran's theoremouter inverse of a matrixrank substractivity

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24) Quadratic and bilinear forms, inner products (15A63)

Related Items (6)

On the Distribution of Matrix Quadratic Forms ⋮ On additive and block decompositions of WLSEs under a multiple partitioned regression model ⋮ Wishartness and independence of matrix quadratic forms in a normal random matrix ⋮ Equalities and inequalities for inertias of Hermitian matrices with applications ⋮ Some equalities for estimations of variance components in a general linear model and its restricted and transformed models ⋮ On the equivalence of estimations under a general linear model and its transformed models

Cites Work

• A further algebraic version of Cochran's theorem and matrix partial orderings
• Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures
• On a matrix version of Cochran's statistical theorem
• Properties of normalr-potent matrices
• Some results concerning normalr- potent operators
• Conditions for Wishartness and Independence of Second Degree Polynomials in a Normal Vector
• Some Matrix Results and Extensions of Cochran’s Theorem
• On the distribution of quadratic forms in normal random variables
• Characterizations of r-potent matrices

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