Matrix Inequalities and Matrix Equations: Theory and Applications

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

Deadline for manuscript submissions: 31 October 2026 | Viewed by 783

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Special Issue Information

Dear Colleague,

Matrix inequalities and matrix equations are central research topics in matrix analysis and applied mathematics, with broad applications in control theory, optimization, signal processing, quantum mechanics, machine learning, and beyond. Recent advancements in high-dimensional data analysis, complex system modeling, and intelligent algorithm design have driven continuous innovation in the theory and computational methods of matrix inequalities and equations, making them a hotspot for interdisciplinary research. 

Topics of interest include, but are not limited to, the following: matrix inequalities, operator inequalities, matrix equations, Lyapunov equations, Riccati equations, matrix norms, trace inequalities, eigenvalue inequalities, matrix convex functions, non-Hermitian matrices, linear matrix inequalities (LMIs), semidefinite programming (SDP), matrix decomposition, iterative algorithms, Krylov subspace methods, low-rank approximation, tensor network algorithms, and stochastic gradient methods.

This Special Issue aims to collate cutting-edge research on matrix inequalities and matrix equations, bridging theoretical advancements and practical innovations.

Prof. Dr. Qing-Wen Wang
Guest Editor

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Keywords

  • matrix inequalities
  • operator inequalities
  • linear matrix inequalities
  • matrix analysis
  • matrix equations
  • matrix decomposition
  • low-rank approximation

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Published Papers (1 paper)

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Research

27 pages, 358 KB  
Article
On Quasilinear Algebra of Linear Interval Equations and Interval Cramer’s Rule
by Yılmaz Yılmaz
Mathematics 2026, 14(6), 1018; https://doi.org/10.3390/math14061018 - 17 Mar 2026
Viewed by 245
Abstract
Determining the solution set of a system of linear interval equations is often a difficult task. Establishing a general theory that includes the classical theory of systems of linear equations as a special case opens the door to extensive and challenging research. In [...] Read more.
Determining the solution set of a system of linear interval equations is often a difficult task. Establishing a general theory that includes the classical theory of systems of linear equations as a special case opens the door to extensive and challenging research. In this study, we aim to develop results concerning the solution sets of such systems by employing the concept of quasilinear spaces. First, we define the determinant of an interval matrix as an interval and its rank as a pair of natural numbers. Then, we introduce the concept of a quasi-inverse for interval matrices and derive several results based on this notion. Using these results, we prove a theorem, which we call the interval Cramer’s rule, concerning the solutions of certain linear interval equation systems. In addition, with respect to the existence of solutions for this type of equation, we present a theorem related to the rank of the interval matrix that models the system. Full article
(This article belongs to the Special Issue Matrix Inequalities and Matrix Equations: Theory and Applications)
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