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Advances of Linear and Multilinear Algebra
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Advances of Linear and Multilinear Algebra

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 2097

Special Issue Editor

Prof. Dr. Abror Khudoyberdiyev

E-Mail Website
Guest Editor
V.I.Romanovsky Institute of Mathematics of the Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan
Interests: non-associative algebras; linear algebra; derivations; degenerations; classifications

Special Issue Information

Dear Colleagues,

This Special Issue entitled “Advances of Linear and Multilinear Algebra” endeavors to publish research papers of the highest quality, with an appeal to specialists in the field of linear and abstract algebra, and to the broad mathematical community. We hope that the distinctive aspects of this Special Issue will bring the reader close to the subject of current research and leave the way open for a more direct and less ambivalent approach to the topic.

Our goal is to invite authors to present their original articles, as well as review articles, that will stimulate continuing efforts to develop new results in these areas of interest. We hope that this Special Issue will have a great impact on other people in their efforts to broaden their knowledge and investigation and help researchers to summarize the most recent developments and ideas in these fields.

This Special Issue invites authors to present their original articles that not only provide new results or methods but may also have a great impact on other people in their efforts to broaden their knowledge and investigation.

Prof. Dr. Abror Khudoyberdiyev
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • linear algebra
  • linear transformations
  • non-associative algebras
  • derivations of algebras
  • degenerations
  • deformations
  • classifications of algebras

Published Papers (3 papers)

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Research

28 pages, 408 KiB  
Article
On Lagrangian Grassmannian Variety and Plücker Matrices
by Jesús Carrillo-Pacheco
Mathematics 2024, 12(6), 858; https://0-doi-org.brum.beds.ac.uk/10.3390/math12060858 - 14 Mar 2024
Viewed by 480
Abstract
The Plücker matrix BL(n,E) of the Lagrangian Grassmannian L(n,E), is determined by the linear envelope ⟨L(n,E)⟩ of the Lagrangian Grassmannian. The linear envelope [...] Read more.
The Plücker matrix BL(n,E) of the Lagrangian Grassmannian L(n,E), is determined by the linear envelope ⟨L(n,E)⟩ of the Lagrangian Grassmannian. The linear envelope ⟨L(n,E)⟩ is the intersection of linear relations of Plücker of Lagrangian Grassmannian, defined here. The Plücker matrix BL(n,E) is a direct sum of the incidence matrix of the configuration of subsets. These matrices determine the isotropy index rn and rn-atlas which are invariants associated with the symplectic vector space E. Full article
(This article belongs to the Special Issue Advances of Linear and Multilinear Algebra)
16 pages, 275 KiB  
Article
A Representation of the Drazin Inverse for the Sum of Two Matrices and the Anti-Triangular Block Matrices
by Li Guo, Guangli Hu, Deyue Yu and Tian Luan
Mathematics 2023, 11(17), 3661; https://0-doi-org.brum.beds.ac.uk/10.3390/math11173661 - 24 Aug 2023
Viewed by 538
Abstract
In this paper, a new formula for the Drazin inverse for the Sum of Two Matrices is given under conditions weaker than those used in some current literature. Further, we apply our results to obtain new representations for the Drazin inverse of an [...] Read more.
In this paper, a new formula for the Drazin inverse for the Sum of Two Matrices is given under conditions weaker than those used in some current literature. Further, we apply our results to obtain new representations for the Drazin inverse of an anti-triangular block matrix under some conditions, which also extend some existing results. Full article
(This article belongs to the Special Issue Advances of Linear and Multilinear Algebra)
18 pages, 300 KiB  
Article
Parallel Sum of Bounded Operators with Closed Ranges
by Wenting Liang
Mathematics 2023, 11(13), 2897; https://0-doi-org.brum.beds.ac.uk/10.3390/math11132897 - 28 Jun 2023
Viewed by 596
Abstract
Let H be a separable infinite dimensional complex Hilbert space and B(H) be the set of all bounded linear operators on H. In this paper, we present several conditions under which the distributive law of the parallel sum is [...] Read more.
Let H be a separable infinite dimensional complex Hilbert space and B(H) be the set of all bounded linear operators on H. In this paper, we present several conditions under which the distributive law of the parallel sum is valid. It is proved that the parallel sum for positive operators with closed ranges is continued at 0. For A,B∈B(H) with closed ranges, it is proved that A≤¯B if and only if A and B−A are parallel summable with the parallel sum A:(B−A)=0, where the symbol “≤¯” denotes the minus partial order. Full article
(This article belongs to the Special Issue Advances of Linear and Multilinear Algebra)
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