47 research outputs found
A method of finding bases of a matrix
The article contains no abstrac
A note on the matrix ordering of special C-matrices
AbstractThe matrix inequality (∗) Δt − tt′ ⩽ Δr − rr′ is considered, where t and r are positive stochastic vectors, and Δt and Δr are diagonal matrices with t and r on their diagonals. Necessary and sufficient conditions are established (1) for (∗) to hold when t and r are given, and (2) for the existence of some vector r satisfying (∗) when t is given. The results have applications in various parts of statistics
On the Löwner, minus, and star partial orderings of nonnegative definite matrices and their squares
Estimability of linear parametric functions in a one-dimensional linear model with restrictions
ArtykuÅ‚ nie zawiera streszczeniaThe problem of estimability of the vector Cξ in the general linear model Ey=Xξ is discussed. It is assumed that the vector of parameters ξ is a linear manifold Ω given by Rξ=s, where the matrix R and the vector s are known. The vector Cξ is estimable if there exist matrices L and M such that ELy+Ms=Cξ for all ξ in Ω. Using the results of a paper by the authors [62046 above], necessary and sufficient conditions for estimability are presented with short and elegant proofs