Ordering of nonnegative definite matrices with application to comparison of linear models

Stępniak, Czesław

doi:10.1016/0024-3795(85)90043-6

Cited by 49 publications

(6 citation statements)

References 3 publications

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“…Different applications of partial orders in many areas, such as statistics, generalized inverses, electrical networks, etc. can be found in [3,4,24,26,28].…”

Section: Introductionmentioning

confidence: 99%

The star partial order and the eigenprojection at 0 on EP matrices

Hernández

Lattanzi

Thome

et al. 2012

Applied Mathematics and Computation

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The star partial order and the eigenprojection at 0 on EPThe space of n × n complex matrices with the star partial order is considered in the first part of this paper. The class of EP matrices is analyzed and several properties related to this order are given. In addition, some information about predecessors and successors of a given EP matrix is obtained. The second part is dedicated to the study of some properties that relate the eigenprojection at 0 with the star and sharp partial orders.

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“…Different applications of partial orders in many areas, such as statistics, generalized inverses, electrical networks, etc. can be found in [3,4,24,26,28].…”

Section: Introductionmentioning

confidence: 99%

The star partial order and the eigenprojection at 0 on EP matrices

Hernández

Lattanzi

Thome

et al. 2012

Applied Mathematics and Computation

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“…Most of the authors present different kinds of generalized inverses following mainly on Moore-Penrose inverses. [1,2,10,12] present the result involving partial orders on matrices. Drazin [5] presented the concept of Star partial ordering * ≤, Hartwig [6] introduced the notion of minus partial order ≤ − , Mitra [9] presented the concept of Sharp partial order ≤ # , left star ordering * ≤ and right star ordering ≤ * .…”

Section: Introductionmentioning

confidence: 99%

Partial Ordering of Block Matrices in Minkowski Space

Krishnaswamy

2021

Comm. Math. Appl.

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“…Since we expect that maps preserving the Löwner order in both directions on the set of all real positive semidefinite matrices may have interesting applications in statistics (e.g. in the theory of comparison of linear models [32]), we will study such maps in Section 3. We will show that a similar result to Molnár's Theorem 1 from [25] holds also in the real matrix case, i.e.…”

Section: Introductionmentioning

confidence: 99%

Preservers of partial orders on the set of all variance-covariance matrices

Golubić

Marovt

2020

Filomat

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Let H+n(R) be the cone of all positive semidefinite n x n real matrices. Two of the best known partial orders that were mostly studied on subsets of square complex matrices are the L?wner and the minus partial orders. Motivated by applications in statistics we study these partial orders on H+n(R). We describe the form of all surjective maps on H+ n (R), n > 1, that preserve the L?wner partial order in both directions. We present an equivalent definition of the minus partial order on H+n(R) and also characterize all surjective, additive maps on H+ n (R), n ? 3, that preserve the minus partial order in both directions.

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Ordering of nonnegative definite matrices with application to comparison of linear models

Cited by 49 publications

References 3 publications

The star partial order and the eigenprojection at 0 on EP matrices

The star partial order and the eigenprojection at 0 on EP matrices

Partial Ordering of Block Matrices in Minkowski Space

Preservers of partial orders on the set of all variance-covariance matrices

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