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Axioms
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Advances in Linear Algebra with Applications
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Special Issue "Advances in Linear Algebra with Applications"

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Algebra and Number Theory".

Deadline for manuscript submissions: 26 February 2024 | Viewed by 2786

Special Issue Editor

Prof. Dr. Jorge Delgado Gracia

E-Mail Website
Guest Editor
Departamento de Matemática Aplicada/IUMA, Universidad de Zaragoza, 50009 Zaragoza, Spain
Interests: numerical linear algebra; computer aided geometric design; approximation theory; numerical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Linear Algebra is the discipline of mathematics dealing with linear equations, linear maps, and their representations in vector spaces and through matrices. The Gaussian elimination procedure can be considered the birth of the discipline. Systems of linear equations were related to what is now called Cartesian geometry. In this sense, lines and planes are represented by linear equations, and their intersections can be computed by solving systems of linear equations. Linear algebra has undergone  great development since its beginnings, extending its applications beyond Cartesian geometry.

Nowadays, Linear Algebra has a lot of applications in all the sciences and in most of the engineering branches. In particular, they are used to deal with important problems in statistics, such as Markov Chains, in the deterministic and stochastic modelling of systems, in Economics, in Data Science, in Signal Processing, in Mathematical Biology, in Graph Theory, and in many others.

In turn, Multilinear Algebra extends the methods of linear algebra. The paper of matrices in linear algebra is played by tensors in multilinear algebra. It also has many applications in many different fields.

The main purpose of this Special Issue of Axioms is to gather recent results with applications of linear and multilinear algebra. In this sense, the application of methods of numerical linear algebra in Science, Engineering, and Economics are welcome.

We cordially invite you to present your recent contributions to this Special Issue.

Prof. Dr. Jorge Delgado Gracia
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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • matrix theory
  • tensor theory
  • numerical methods in linear algebra
  • structured matrices and tensors
  • direct and iterative solution methods
  • accuracy methods in linear algebra
  • applications of linear algebra

Published Papers (4 papers)

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Research

16 pages, 305 KiB  
Article
T-BT Inverse and T-GC Partial Order via the T-Product
by
Hongxing Wang
and
Wei Wen
Axioms 2023, 12(10), 929; https://doi.org/10.3390/axioms12100929 - 28 Sep 2023
Viewed by 314
Abstract
In this paper, we extend the BT inverse to the set of third-order tensors, and we call it the T-BT inverse. We give characterizations and properties of the inverse by applying tensor decomposition. Based on the inverse, we introduce a new binary relation: [...] Read more.
In this paper, we extend the BT inverse to the set of third-order tensors, and we call it the T-BT inverse. We give characterizations and properties of the inverse by applying tensor decomposition. Based on the inverse, we introduce a new binary relation: T-BT order. Furthermore, by applying the T-BT order, we introduce a generalized core partial order (called T-GC partial order). Full article
(This article belongs to the Special Issue Advances in Linear Algebra with Applications)
17 pages, 616 KiB  
Article
On the Total Positivity and Accurate Computations of r-Bell Polynomial Bases
by
Esmeralda Mainar
,
Juan Manuel Peña
and
Beatriz Rubio
Axioms 2023, 12(9), 839; https://doi.org/10.3390/axioms12090839 - 29 Aug 2023
Viewed by 436
Abstract
A new class of matrices defined in terms of r-Stirling numbers is introduced. These r-Stirling matrices are totally positive and determine the linear transformation between monomial and r-Bell polynomial bases. An efficient algorithm for the computation to high relative accuracy [...] Read more.
A new class of matrices defined in terms of r-Stirling numbers is introduced. These r-Stirling matrices are totally positive and determine the linear transformation between monomial and r-Bell polynomial bases. An efficient algorithm for the computation to high relative accuracy of the bidiagonal factorization of r-Stirling matrices is provided and used to achieve computations to high relative accuracy for the resolution of relevant algebraic problems with collocation, Wronskian, and Gramian matrices of r-Bell bases. The numerical experimentation confirms the accuracy of the proposed procedure. Full article
(This article belongs to the Special Issue Advances in Linear Algebra with Applications)
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16 pages, 618 KiB  
Article
Green Matrices, Minors and Hadamard Products
by
Jorge Delgado
,
Guillermo Peña
and
Juan Manuel Peña
Axioms 2023, 12(8), 774; https://doi.org/10.3390/axioms12080774 - 10 Aug 2023
Viewed by 759
Abstract
Green matrices are interpreted as discrete version of Green functions and are used when working with inhomogeneous linear system of differential equations. This paper discusses accurate algebraic computations using a recent procedure to achieve an important factorization of these matrices with high relative [...] Read more.
Green matrices are interpreted as discrete version of Green functions and are used when working with inhomogeneous linear system of differential equations. This paper discusses accurate algebraic computations using a recent procedure to achieve an important factorization of these matrices with high relative accuracy and using alternative accurate methods. An algorithm to compute any minor of a Green matrix with high relative accuracy is also presented. The bidiagonal decomposition of the Hadamard product of Green matrices is obtained. Illustrative numerical examples are included. Full article
(This article belongs to the Special Issue Advances in Linear Algebra with Applications)
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12 pages, 804 KiB  
Article
Tensor Eigenvalue and SVD from the Viewpoint of Linear Transformation
by
Xinzhu Zhao
,
Bo Dong
,
Bo Yu
and
Yan Yu
Axioms 2023, 12(5), 485; https://doi.org/10.3390/axioms12050485 - 17 May 2023
Viewed by 738
Abstract
A linear transformation from vector space to another vector space can be represented as a matrix. This close relationship between the matrix and the linear transformation is helpful for the study of matrices. In this paper, the tensor is regarded as a generalization [...] Read more.
A linear transformation from vector space to another vector space can be represented as a matrix. This close relationship between the matrix and the linear transformation is helpful for the study of matrices. In this paper, the tensor is regarded as a generalization of the matrix from the viewpoint of the linear transformation instead of the quadratic form in matrix theory; we discuss some operations and present some definitions and theorems related to tensors. For example, we provide the definitions of the triangular form and the eigenvalue of a tensor, and the theorems of the tensor QR decomposition and the tensor singular value decomposition. Furthermore, we explain the significance of our definitions and their differences from existing definitions. Full article
(This article belongs to the Special Issue Advances in Linear Algebra with Applications)
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