-
Strictly monotone sequences of lower and upper bounds on Perron values and their combinatorial applications Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-04-17 Sooyeong Kim, Minho Song
In this paper, we present monotone sequences of lower and upper bounds on the Perron value of a nonnegative matrix, and we study their strict monotonicity. Using those sequences, we provide two com...
-
Fixed point groups of involutions of type O(q,k) over a field of characteristic two Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-04-15 Mark Hunnell, John Hutchens
For G=O(q,k), the orthogonal group over a field k of characteristic 2 with respect to a quadratic form q, we discuss the G-conjugacy classes of fixed points of involutions. When the quadratic spac...
-
Computing a compact local Smith–McMillan form Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-04-15 Vanni Noferini, Paul Van Dooren
We define a compact local Smith–McMillan form of a rational matrix R(λ) as the diagonal matrix whose diagonal elements are the nonzero entries of a local Smith-McMillan form of R(λ). We show that a...
-
Generalized matricial ranges and positive definiteness Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-04-08 Yiu-Tung Poon, Nyle Alexander Sutton
Numerical range is the subject of study for over a century. Its extension to matricial range is defined in terms of completely positive maps. A linear map ϕ between matrix algebras is completely po...
-
A novel structure-preserving algorithm for the singular value decomposition of biquaternion matrices Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-04-01 Wenxv Ding, Anli Wei, Ying Li, Mingcui Zhang, Zhihong Liu
In this paper, we study the singular value decomposition of biquaternion matrices. We prove that the singular value decomposition of biquaternion matrices can be equivalently converted to the singu...
-
VDR decomposition of Chebyshev-Vandermonde matrices with the Arnoldi Process Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-04-01 Ik-Pyo Kim, Arnold R. Kräuter
This paper introduces the VDR decomposition of Chebyshev-Vandermonde matrices, where V represents an ordinary Vandermonde matrix, D is diagonal, and R is upper triangular. Our motivation for this w...
-
On the M2,A,A-numerical range and the M2,A,A-maximal numerical range of the basic elementary operator M2,B,C Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-03-25 Zakaria Taki
Let A be a positive bounded operator acting on a complex Hilbert space H. For two bounded operators B and C on H, we denote by M2,B,C the basic elementary operator on the class of Hilbert–Schmidt o...
-
Ordering of graphs with fixed size and diameter by Aα-spectral radii Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-03-21 Wei Wei, Zhimin Feng
The Aα-matrix of a graph G is defined as the convex linear combination of the adjacency matrix A(G) and the diagonal matrix of degrees D(G), i.e. Aα(G)=αD(G)+(1−α)A(G) with α∈[0,1]. The maximum mod...
-
The kernels of powers of linear operator via Weyr characteristic Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-03-19 Jie Jian, Jun Liao, Heguo Liu
The adjoint of a matrix in the Lie algebra associated with a matrix algebra is a fundamental operator, which can be generalized to a more general operator φAB:X→AX−XB by two matrices A and B. The k...
-
The Jordan algebraic structure of the rotated quadratic cone Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-03-21 Baha Alzalg, Karima Tamsaouete, Lilia Benakkouche, Ayat Ababneh
In this paper, we look into the rotated quadratic cone and analyze its algebraic structure. We construct an algebra associated with this cone and show that this algebra is a Euclidean Jordan algebr...
-
Generalizing Choi map in M3 beyond circulant scenario Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-03-18 Anindita Bera, Giovanni Scala, Gniewomir Sarbicki, Dariusz Chruściński
We introduce a family of positive linear maps in the algebra of 3×3 complex matrices, which generalizes the seminal positive non-decomposable map originally proposed by Choi. Necessary and sufficie...
-
Modified CRI iteration methods for complex symmetric indefinite linear systems Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-03-12 Zhao-Zheng Liang, Yan Dou
This work investigates the iterative solution of complex symmetric linear systems with indefinite matrix term. Based on a technical equivalent reformulation of the original indefinite systems, an e...
-
On an analogue of a property of singular M-matrices for the Lyapunov and Stein operators Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-03-12 A.M. Encinas, S. Mondal, K.C. Sivakumar
A well-known result for a singular irreducible M-matrix A is that the only nonnegative vector that belongs to the range space of A is the zero vector. In this paper, we prove an analogue of this re...
-
Countably many asymptotic tensor ranks Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-03-12 Andreas Blatter, Jan Draisma, Filip Rupniewski
In connection with recent work on gaps in the asymptotic subranks of complex tensors the question arose whether the number of nonnegative real numbers that arise as the asymptotic subrank of some c...
-
Rank one quaternionic operators and additive preservers Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-03-11 E. M. Ouahabi, K. Souilah
In this paper, we completely describe all additive surjective maps, on the set of all bounded finite rank right linear operators acting on a right quaternionic Banach space, that preserve the set o...
-
Lie triple centralizers of the algebra of dominant block upper triangular matrices Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-03-04 Prakash Ghimire, Magdalena Benavides, Sheral King, Lavona Young
Let N be the algebra of all n×n dominant block upper triangular matrices over a field. In this paper, we explicitly describe all Lie triple centralizers of N. We also describe Lie triple centralize...
-
Distance spectral radius and fractional matching in t-connected graphs Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-03-04 Yanling Hu, Huiqiu Lin, Yuke Zhang, Zhiguo Zhang
A fractional matching of a graph G is a function f assigning each edge a number in [0,1] so that ∑e∈Γ(v)f(e)≤1 for each v∈V(G), where Γ(v) is the set of edges incident to v. The fractional matching...
-
Probabilistic bounds on best rank-1 approximation ratio Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-03-03 Khazhgali Kozhasov, Josué Tonelli-Cueto
We provide new upper and lower bounds on the minimum possible ratio of the spectral and Frobenius norms of a (partially) symmetric tensor. In the particular case of general tensors, our result reco...
-
A note on a generalized Jordan form of an infinite upper triangular matrix Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-21 Adel Abyzov, Alexander Maklakov
In this paper, several equivalent conditions for the existence of a generalized Jordan form for matrices of locally nilpotent linear operators acting on an infinite countable dimensional vector spa...
-
Existence and uniqueness of solutions for Leontief's Input–Output Model, graph theory and sensitivity analysis Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-20 José Carlos Bellido, Luis Felipe Prieto-Martínez
We provide a complete study of existence and uniqueness (uniqueness up to multiples in the case d=0) of non-negative and non-trivial solutions x for the linear system (I−A)x=d with A≥0,d≥0 (which, ...
-
G-Drazin inverse combined with inner inverse Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-14 G. Maharana, J. K. Sahoo, Néstor Thome
This article introduces new classes of generalized inverses for square matrices named GD1, and the dual, called 1GD inverse. In addition, we discuss a few characterizations and representations of t...
-
Minimizers for the energy of eccentricity matrices of trees Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-13 Iswar Mahato, M. Rajesh Kannan
The eccentricity matrix of a connected graph G, denoted by E(G), is constructed from the distance matrix of G by keeping only the largest nonzero elements in each row and each column and setting th...
-
A new closed-form expression for the solution of ODEs in a ring of distributions and its connection with the matrix algebra Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-11 S. Pozza
A new expression for solving homogeneous linear ODEs based on a generalization of the Volterra composition was recently introduced. In this work, we extend such an expression, showing that it corre...
-
Independence and orthogonality of algebraic eigenvectors over the max-plus algebra Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-12 Yuki Nishida, Sennosuke Watanabe, Yoshihide Watanabe
The max-plus algebra R∪{−∞} is a semiring with the two operations: addition a⊕b:=max(a,b) and multiplication a⊗b:=a+b. Roots of the characteristic polynomial of a max-plus matrix are called algebra...
-
Symmetric Hamiltonian vector fields Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-12 P. H. Baptistelli, M. E. R. Hernandes, E. M. Terezio
In this work, we present algebraic results for Hamiltonian and symmetric vector fields on 2n-dimensional symplectic vector spaces. Our main results are in the linear context. In the case n = 1, we ...
-
Unitary equivalences for k-circulant operator matrices with applications Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-07 Ozra Abdollahi, Saeed Karami, Jamal Rooin, Mohammad Hossein Sattari
Let k and n be two coprime positive integers. In this paper, we show that any n×n k-circulant operator matrix Ak,n with the first row A1,…,An∈B(H) is unitarily equivalent to a generalized permutati...
-
Characterizing matrices with eigenvalues in an LMI region: a dissipative-Hamiltonian approach Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-07 Neelam Choudhary, Nicolas Gillis, Punit Sharma
In this paper, we provide a dissipative Hamiltonian (DH) characterization for the set of matrices whose eigenvalues belong to a given LMI region. This characterization is a generalization of that o...
-
Inner product inequalities with applications Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-07 Mohammad Sababheh, Hamid Reza Moradi, Satyajit Sahoo
In this paper, we show some inner product inequalities, which can be considered of Cauchy-Schwarz and Buzano type inequalities for Hilbert space operators. This will lead to several applications th...
-
Divisibility among power matrices associated with multiplicative functions Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-07 Siao A. Hong, Guangyan Y. Zhu
Let a, b and n be positive integers and let S={x1,…,xn} be a set of n distinct positive integers. For x∈S, one defines GS(x)={y∈S:y
-
Characterization of self-adjoint domains for regular odd order C-symmetric differential operators Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-05 Qinglan Bao, Jiong Sun, Xiaoling Hao
We enlarge the class of regular odd order differential operators and find the self-adjoint boundary condition of every operator. In this paper, we give the characterization of self-adjoint domains ...
-
The generalized sectorial decompositions of semi-sectorial operators Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-02 Yuwen Liu, Liu Liu, Yufeng Lu
This paper considers the generalized sectorial decompositions of semi-sectorial operators and quasi-sectorial operators on the complex Hilbert space. Under an invariant subspace condition, a necess...
-
Forms of biisometric operators and biorthogonality Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-06 B. P. Duggal, C. S. Kubrusly
The paper proves two results involving a pair (A,B) of P-biisometric or (m,P)-biisometric Hilbert-space operators for arbitrary positive integer m and positive operator P. It is shown that if A and...
-
Structured backward errors for block three-by-three saddle point systems Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-02 Wei Ma, Yadan Fan, Xiaoyi Xu
In this paper, we analyze the structured backward error for block three-by-three saddle point systems. The computable formulas of structured backward errors are derived, which are useful for testin...
-
Chow's theorem for Hilbert Grassmannians as a Wigner-type theorem Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-02-02 Mark Pankov, Adam Tyc
Let H be an infinite-dimensional complex Hilbert space. Denote by G∞(H) the Grassmannian formed by closed subspaces of H whose dimension and codimension both are infinite. We say that X,Y∈G∞(H) are...
-
Tight infinite matrices Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-29 Ron Aharoni, He Guo
We give a simple proof of a recent result of Gollin and Joó (Matching variables to equations in infinite linear equation systems. Linear Algebra Appl. 2023;660:40–46. doi: 10.1016/j.laa.2022.12.002...
-
Multiple 2-summing operators from a Cartezian product of l1(H)-spaces with values in a Hilbert space Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-31 Dumitru Popa
We use the Maurey–Rosenthal factorization theorem to give the necessary and sufficient conditions that an operator on the Cartezian product of l1(H)-spaces with values in a Hilbert space to be mult...
-
Euclidean and circum-Euclidean distance matrices: characterizations and interlacing property Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-25 I. Jeyaraman, T. Divyadevi
Motivated by the inverse formula of the distance matrix of a tree and the Moore–Penrose inverse of a circum-Euclidean distance matrix (CEDM), in this paper, we study a general real square matrix M ...
-
Endomorphisms of the riordan group, some new facts Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-25 R. Słowik
We consider endomorphisms of the Riordan group. This issue was recently studied by Petrullo and Senato who gave the characterization of these endomorphisms in terms of endomorphisms of the Appell a...
-
Upper and lower bounds for the solution of the Lyapunov matrix differential equation Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-25 Jianzhou Liu, Ze Zhang, Wenlong Zeng, Fuying Tang
In control systems, the study of controllability, observability and stability can often be transformed into the estimation of the upper and lower bounds for the solution of the Lyapunov matrix diff...
-
On the construction of MRD convolutional codes Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-22 Diego Napp, Raquel Pinto, Filipa Santana, Carlos Vela
The problem of building optimal block codes, such as MDS codes, over small fields has been an active area of research that led to several interesting conjectures. In the context of convolutional co...
-
A new invariant for cyclic orbit flag codes Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-22 Clementa Alonso-González, Miguel Ángel Navarro-Pérez
In the network coding framework, given a prime power q and the vector space Fqn, a constant type flag code is a set of nested sequences of Fq-subspaces (flags) with the same increasing sequence of ...
-
On a question of Erdős on doubly stochastic matrices Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-22 Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin
In a celebrated paper of Marcus and Ree [M. Marcus, R. Ree. Diagonals of doubly stochastic matrices. Quart J Math Oxford Ser. 1959; 10(1):296–302], it was shown that if A=[aij] is an n×n doubly sto...
-
Level numbers of a bounded linear operator between normed linear spaces-II Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-18 Saikat Roy, Debmalya Sain, Ryotaro Tanaka
We continue the study of level numbers and level vectors of a bounded linear operator between normed linear spaces. We prove that every linear operator on a finite-dimensional polyhedral Banach spa...
-
Parametrizing spectral filters for nonsingular polynomial matrices Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-18 Agurtzane Amparan, Silvia Marcaida, Ion Zaballa
Two polynomial matrices are spectrally equivalent if they have the same finite and infinite elementary divisors. Spectral equivalence can be characterized using very special polynomial matrices cal...
-
Exposedness of elementary positive maps between matrix algebras Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-18 Seung-Hyeok Kye
The positive linear maps Ads which send matrices x to s∗xs play important roles in quantum information theory as well as matrix theory. It was proved by [Marciniak M. Rank properties of exposed pos...
-
High relative accuracy for rational q-Bernstein–Vandermonde matrices Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-18 Jorge Delgado, Héctor Orera, J. M. Peña
In this article, an accurate and efficient method to compute the eigenvalues, singular values and inverses of nonsingular totally positive rational q-Bernstein–Vandermonde matrices and the solution...
-
A note on products of idempotents in the ring of upper triangular infinite matrices Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-16 Roksana Słowik
It is known that every singular matrix of a finite degree defined over a field can be written as a product of a finite number of idempotent matrices. Insipired by this result we investigate the sam...
-
Some properties of combinatorial triangles related to Horadam polynomials Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-16 Yu Wang, Jinyang Zhang, Huyile Liang
The Horadam polynomials unify many well-known polynomials, such as the Fibonacci polynomials, the Lucas polynomials, the Pell polynomials, the Jacobsthal polynomials and the Chebyshev polynomials. ...
-
Conjugate phase retrieval on general Hilbert spaces Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-07 Ya-Nan Li, Yun-Zhang Li
A conjugation on a Hilbert space H means an antilinear bounded operator that the squares to the identity, which generalizes the traditional conjugation on complex Euclidean spaces. In this paper, w...
-
Symmetric ideals of generalized summing multilinear operators Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-07 Geraldo Botelho, Ariel S. Santiago
Let X1,…,Xn,Y be classes of Banach spaces-valued sequences. An n-linear operator A between Banach spaces belongs to the ideal of (X1,…,Xn;Y)-summing multilinear operators if (A(xj1,…,xjn))j=1∞ belo...
-
Upper bounds for the Euclidean spectral radius of operators via joint norms Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-10 Najla Altwaijry, Silvestru Sever Dragomir, Kais Feki
Let re(S) be the Euclidean spectral radius associated with a q-tuple S=(S1,…,Sq) of bounded linear operators on a complex Hilbert space. The principal objective of our study is to establish vario...
-
Berezin number and Berezin norm inequalities for operator matrices Linear Multilinear Algebra (IF 1.1) Pub Date : 2024-01-02 Pintu Bhunia, Anirban Sen, Somdatta Barik, Kallol Paul
We establish new upper bounds for the Berezin number and Berezin norm of operator matrices, which are refinements of existing bounds. Among other bounds, we prove that if A=[Aij] is an n×n operator...
-
The Wasserstein mean of unipotent matrices Linear Multilinear Algebra (IF 1.1) Pub Date : 2023-12-26 Sejong Kim, Vatsalkumar N. Mer
We define the Wasserstein mean of n×n unipotent matrices by solving its corresponding matrix equation, and study its fundamental properties. Under a binomial expansion for the weighted geometric me...
-
Norm and numerical radius inequalities for operator matrices Linear Multilinear Algebra (IF 1.1) Pub Date : 2023-12-27 Fuad Kittaneh, Hamid Reza Moradi, Mohammad Sababheh
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator no...
-
Convex-cyclic weighted translations on locally compact groups Linear Multilinear Algebra (IF 1.1) Pub Date : 2023-12-26 M. R. Azimi, I. Akbarbaglu, M. Asadipour
A bounded linear operator T on a Banach space X is called a convex-cyclic operator if there exists a vector x∈X such that the convex hull of Orb(T,x) is dense in X. In this paper, for given an aper...
-
Bisymmetric non-negative Jacobi matrix realizations Linear Multilinear Algebra (IF 1.1) Pub Date : 2023-12-21 A.M. Encinas, M.J. Jiménez, C. Marijuán, M. Mitjana, M. Pisonero
Within the symmetric inverse eigenvalue problem, the case of bisymmetric Jacobi matrices occupies a central place, since for any strictly monotone list of n real numbers there exists a unique bisym...
-
Zeta functions of signed graphs Linear Multilinear Algebra (IF 1.1) Pub Date : 2023-12-19 Deqiong Li, Yaoping Hou, Dijian Wang
We introduce the zeta function of a signed graph and give a determinant expression for it in terms of the signed oriented line graph, and moreover, we obtain some properties of the zeta function of...
-
The solution of the Loewy–Radwan conjecture Linear Multilinear Algebra (IF 1.1) Pub Date : 2023-11-30 Matjaž Omladič, Klemen Šivic
A seminal result of Gerstenhaber gives the maximal dimension of a linear space of nilpotent matrices. It also exhibits the structure of such a space when the maximal dimension is attained. Extensio...
-
Some inequalities about Bourin's question in noncommutative Lp-spaces Linear Multilinear Algebra (IF 1.1) Pub Date : 2023-11-29 Jinchen Liu, Kan He, Liang Liu
This paper studies a question of Bourin on noncommutative Lp spaces. Some inequalities due to Hayajneh et al. [Norm inequalities for positive semidefinite matrices and a question of Bourin II. Int ...
-
On the eigenvectors of generalized circulant matrices Linear Multilinear Algebra (IF 1.1) Pub Date : 2023-11-24 Enide Andrade, Dante Carrasco-Olivera, Cristina Manzaneda
In this paper, closed formulas for the eigenvectors of a particular class of matrices generated by generalized permutation matrices, named generalized circulant matrices, are presented.