Currently displaying 1 – 5 of 5

Showing per page

Order by Relevance | Title | Year of publication

On orderings induced by the Loewner partial ordering

Jan HaukeAugustyn Markiewicz — 1994

Applicationes Mathematicae

The partial ordering induced by the Loewner partial ordering on the convex cone comprising all matrices which multiplied by a given positive definite matrix become nonnegative definite is considered. Its relation to orderings which are induced by the Loewner partial ordering of the squares of matrices is presented. Some extensions of the latter orderings and their comparison to star orderings are given.

All about the ⊥ with its applications in the linear statistical models

Augustyn MarkiewiczSimo Puntanen — 2015

Open Mathematics

For an n x m real matrix A the matrix A⊥ 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 ⊥ 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

Beyond the MatTriad Conferences

Jan HaukeAugustyn MarkiewiczSimo Puntanen — 2020

Applications of Mathematics

In this article we present a short history of the MatTriad Conferences, a series of international conferences on matrix analysis and its applications. The name MatTriad originally comes from the phrase Three Days Full of Matrices. The first MatTriad was held in the Mathematical Research and Conference Center of the Institute of Mathematics of the Polish Academy of Sciences in Będlewo, near Poznań, Poland, 3–5 March 2005, and has since then been organized biennially. The 8th MatTriad was held in...

Block matrix approximation via entropy loss function

Malwina JaniszewskaAugustyn MarkiewiczMonika Mokrzycka — 2020

Applications of Mathematics

The aim of the paper is to present a procedure for the approximation of a symmetric positive definite matrix by symmetric block partitioned matrices with structured off-diagonal blocks. The entropy loss function is chosen as approximation criterion. This procedure is applied in a simulation study of the statistical problem of covariance structure identification.

Page 1

Download Results (CSV)