This paper presents the reduced biquaternion mixed least squares and total least squares (RBMTLS) method for solving an overdetermined system AX≈B in the reduced biquaternion algebra. The RBMTLS me...

We consider tridiagonal matrices (aij)i,j=1n with constant main diagonal and such that ai,i+1ai+1,i=1 for i=1,…,n−1. For these matrices, criteria are established under which their Kippenhahn curves...

In this study, we explore the interrelation between hypergraph symmetries represented by equivalence relations on the vertex set and the spectra of operators associated with the hypergraph. We intr...

In this paper, we derive some practical necessary and sufficient conditions for the existence of a solution to a new system of coupled two-sided Sylvester-like matrix equations with arbitrary numbe...

We introduce a new elimination procedure for Partition Analysis to obtain generating functions free of Omega variables starting with a crude generating function containing or not factored polynomia...

Solving certain systems of matrix equations, we generalize notions of index-MP, MP-index and MP-index-MP matrices defined for square matrices and we introduce novel types of rectangular matrices, t...

We study the essential numerical range of complex operators on a quaternionic Hilbert space and its relation with the essential S-spectrum. We give a new characterization of the essential numerical...

Let F be a field, p(x) be a quadratic polynomial in F[x] with a non-zero constant term, and n≥2 be a positive integer. We say that T∈Mn(F) is p(x)-quadratic if p(T)=0. In this paper, given A∈SLn(F)...

The property (R) for a bounded linear operator T on a Hilbert space means that the points λ in the approximate point spectrum of T for which T−λI is upper semi-Browder are exactly the isolated poin...

In this paper, we consider the entries of the bottleneck matrices of maximal outerplanar graphs with isomorphic underlying trees. We show how the entries of the bottleneck matrix are perturbed when...

In this paper, we consider relationships between net-regular, strongly regular and walk-regular signed graphs. There is no inclusion between any two of these classes, and we investigate conditions ...

In this article, we focus on the error that is committed when computing the matrix logarithm using the Gauss–Legendre quadrature rules. These formulas can be interpreted as Padé approximants of a s...

This paper is concerned with the closedness (closability), essential spectra and generator properties for a one-sided coupled operator matrix A0 acting in a product of Banach spaces X and Y. By com...

In this paper, we extend the concepts of m-partial isometry of order q and (m,A)-isometry, building on the contributions of Aouichaoui MA. [A note on partial-A-isometries and some applications. Qua...

In this article, Albert Wei's result which described the forms of the linear maps that preserve the set of orthogonal matrices is treated and its new proof is provided. Wei's result is simplified b...

Assume that M is a Hilbert C∗-module over a C∗-algebra A and δ:M→M is a map. It is shown that if δ is A-linear, then the three statements are equivalent: (1) δ is a Jordan derivation; (2) δ is a de...

The smallest positive eigenvalue τ(G) of a simple graph G is the smallest positive eigenvalue of its adjacency matrix A(G). In [F. J. Zhang and A. Chang, Acyclic molecules with greatest HOMO-LUMO s...

A square matrix A is an involution if A2=I. The centralizer of a square matrix S, denoted by C(S), is the set of all matrices A such that AS = SA. Let F be an algebraically closed field of characte...

Let n⩾2 be an integer and let Nn(F) be the algebra of n×n strictly upper triangular matrices over a field F with center Z(Nn(F)). In this paper, we obtain a structural characterization of additive ...

To solve some systems of operator equations, we generalize the concepts of the W–weighted core–EP inverse, the W-gMP inverse, the generalized core–EP inverse and their duals and we define new kinds...

Let A be a semi-finite factor von Neumann algebra. We prove that if a map δ:A→A satisfies that for any A,B∈A there is a linear derivation δA,B:A→A such that δ(A)B+Aδ(B)=δA,B(AB), then δ is a linear...

We investigate two one-sided orthogonalities of matrices, the first of which is left (right) star-orthogonality for rectangular matrices and the other is left (right) core-orthogonality of index 1 ...

A digraph is called oriented if there is at most one arc between two distinct vertices. We call an oriented graph D is nonsingular if its adjacency matrix is nonsingular. In this paper, we characte...

Quaternion algebra H is an extension of the complex number field, which is a noncommutative associative algebra. In recent years, quaternionic Fourier analysis has interested some mathematicians du...

Let G be a simple graph on n vertices, and let λ1,λ2,…,λn be the Laplacian eigenvalues of G. The Laplacian Estrada index of G is defined as LEE(G)=∑i=1neλi. Consider a graph G with n≥3 vertices, m ...

In this article, we corrected the trilinear formula for triple disjoint matrix multiplication given in the article ‘J. Laderman, V. Pan, X. H. Sha, On practical Algorithms for Accelerated Matrix Mu...

The core and core–EP inverses are two recent generalized inverses that were first introduced and studied for complex matrices, and later for elements of rings with involution. Afterward, weighted v...

In this paper, we consider the entries of the bottleneck matrices of maximal outerplanar graphs. We recall patterns from [Kirkland SJ, Neumann M, Shader BL. Characteristic vertices of weighted tree...

This paper studies the concept of stable perturbation B∈Cn×n for the core-EP inverse of a matrix A∈Cn×n with index k. For a given stable perturbation B of A, explicit expressions of its core-EP inv...

Three approximation problems in Krein spaces are studied, namely the indefinite weighted least squares problem and the related problems of indefinite abstract splines and smoothing. In each case, w...

For a graph G with domination number γ, Hedetniemi, Jacobs and Trevisan (2016) proved that mG[0,1)≤γ, where mG[0,1) means the number of Laplacian eigenvalues of G in the interval [0,1). Let T be a ...

In this paper, we characterize additive maps between exterior power of vector spaces that send decomposable multivectors to decomposable multivectors. As an application, we deduce Kuzma's result re...

Spectral hypergraph theory mainly concerns using hypergraph spectra to obtain structural information about the given hypergraphs. The study of cospectral hypergraphs is important since it reveals w...

We determine the exact diameter of the orthograph related to mutual strong Birkhoff–James orthogonality in arbitrary finite-dimensional C∗-algebra. Additionally, we will estimate the distance betwe...

The signed enhanced principal rank characteristic sequence (sepr-sequence) of a given n×n Hermitian matrix B is the sequence t1t2…tn, where tk is A∗, A+, A−, N, S∗, S+, or S−, based on the followin...

Bhatia, Lim and Yamazaki obtained results on the norm minimality of the Kubo-Ando Heinz means of positive semidefinite matrices. Namely, they proved that |||A♯αB+A♯1−αB|||≤|||AαB1−α+A1−αBα|||, for...

Consider a matrix polynomial P(λ)=A0+λA1+⋯+λdAd, with A0,…,Ad complex (or real) matrices with a certain structure. In this paper we discuss an iterative method to numerically approximate the closes...

We present a class of inexact splitting-modulus iteration methods for solving the Pareto Eigenvalue Complementarity Problem (EiCP) when the system matrix A is an H+-matrix. Our method first employs...

By using equivalence conditions for sectorial matrices obtained by Alakhrass and Sababheh in Linear Algebra Appl. (2020;586), we improve a Rotfel'd type inequality for sectorial matrices derived by...

Let T be an operator on a Banach space X that is similar to −T via an involution U. Then,U decomposes the Banach space X as X=X1⊕X2 with respect to which decomposition we have U=(I100−I2), where Ii...

In this note, we introduce a notion of the J-kernel of a bounded linear operator on a Krein space and study the J-Fredholm theory for Krein space operators. Using J-Fredholm theory, we discuss and ...

In any dimension d≥2, we give exact volume formulas of two mutually polar dual convex d-polytopes. The primal body is called isocanted cube of dimension d, depending on two real parameters 0

Let n∈N, K∈{R,C} and Mn(K) be the set of all n-by-n matrices with entries in K. We investigate the sensitivity of the generalized spectral radius ρK(A):=max{|λ|:λ∈Kand|Ax|=|λx|foranx∈Kn∖{0}} of A∈...

Published in Linear and Multilinear Algebra (Ahead of Print, 2024)

We prove that if Δ is a norm-continuous weak∗-2-local derivation on a von Neumann algebra M and satisfies Δ(p+iμq)=Δ(p)+iμΔ(q) for every pair of projections p and q in M, and every μ∈R, then Δ is a...

We present a new method to construct symmetric symbols corresponding to solvable multiscaling equations using linear operators. First, we define a linear operator corresponding to a symbol. We demo...

In this work we focus on the notion of quantum hitting time for discrete-time Szegedy quantum walks, compared to its classical counterpart. Under suitable hypotheses, quantum hitting time is known ...

We prove a lower bound on the dimension of the set of maximal border subrank tensors. This is the first such bound of its type.

Let F be a field, and n≥r>0 be integers, with r even. Denote by An⁡(F) the space of all n-by-n alternating matrices with entries in F. We consider the problem of determining the greatest possible d...

In this article, we investigate explicitly the minimal and maximal values of the α-z-Rényi divergences and some other types of Rényi divergences between unitary orbits. Our main tools are the major...

Let μ be a finite measure, T:L1(μ)→X be an operator into a Banach space X, and I:L∞(μ)→L1(μ) be the natural inclusion. A well-known theorem due to Grothendieck states that T is representable if and...

Let A be a unital C∗-algebra with unit e and let a:b be the parallel sum of the two positive definite elements a and b of A defined by a(a+b)−1b. We show that the parallel sum a:b can be stated by ...

This work classifies three-dimensional simple evolution algebras over arbitrary fields. For this purpose, we use tools such as the associated directed graph, the moduli set, inductive limit group, ...

In this paper, a method for the construction of tridiagonal sign regular (SR) matrices is presented, as well as the necessary conditions to carry out this construction and the characterization of t...

In this paper we obtain a necessary and sufficient condition for an operator on a uniform algebra to be nice. We characterize nice operators on an expansive class of Banach spaces. Then as examples...

This paper introduces the core projection operator inverse and its characterizations. Using this concept, we define the P-core partial order and D-core partial order, along with their properties. T...

In this paper, we consider the unbounded local completely positive and local completely contractive maps on a maximal tensor product of unital locally C∗-algebras and discuss on extremal points of ...

The purpose of this note is to establish logarithmic submajorization inequalities that are associated with von Neumann's trace inequality for operators in finite von Neumann algebras. As an applica...

A square complex matrix A is called (skew) J-Hamiltonian if AJ is (skew) Hermitian where J is a real normal matrix such that J2=−I, where I is the identity matrix. In this paper, we solve the Procr...

This paper's main objective is to find new upper bounds for the norm of the sum of two Hilbert space operators and their Kronecker product. The obtained results extend some previously known results...