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Algebraic technique for mixed least squares and total least squares problem in the reduced biquaternion algebra Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-10-30
Sk. Safique Ahmad, Neha BhadalaThis 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...
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Unified approach to reciprocal matrices with Kippenhahn curves containing elliptical components Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-10-25
Muyan Jiang, Ilya M. SpitkovskyWe 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...
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On some building blocks of hypergraphs Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-10-23
Anirban Banerjee, Samiron ParuiIn 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...
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A new system of sylvester-like matrix equations with arbitrary number of equations and unknowns over the quaternion algebra Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-10-21
Zhuo-Heng He, Andrii Dmytryshyn, Qing-Wen WangIn 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...
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A new approach to MacMahon’s Partition Analysis and associated applications Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-10-17
Antônio Francisco NetoWe 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...
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Weighted index-MP matrices Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-10-09
Dijana Mosić, Daochang ZhangSolving 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...
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Quaternionic essential numerical range of complex operators Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-10-07
Luís Carvalho, Cristina Diogo, Sérgio Mendes, Helena SoaresWe 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...
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Decomposition of matrices into products of commutators of quadratic matrices Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-10-04
M. H. Bien, M. Ramezan-Nassab, L. Q. TruongLet 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)...
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Some new results on the property (R) under compact perturbations Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-10-04
Nan Li, Xiaohong Cao, Jiong DongThe 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...
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Bottleneck matrices of maximal outerplanar graphs with isomorphic underlying trees Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-10-01
Jason J. MolitiernoIn 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...
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Relationships between net regularity, strong regularity and walk regularity of signed graphs Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-09-30
Milica Anđelić, Tamara Koledin, Zoran StanićIn 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 ...
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Theoretical error estimates for computing the matrix logarithm by Padé-type approximants Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-09-24
Lidia Aceto, Fabio DurastanteIn 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...
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Gustafson, Jeribi, Weidmann and Wolf essential spectra and generator properties for one-sided coupled operator matrices Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-09-24
Lei Zhao, Jing Xu, Junjie HuangThis 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...
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Advancements in the generalization of m-isometries: introducing the q-partial-(m, A)-isometry class Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-09-20
Sid Ahmed Ould Ahmed Mahmoud, Mohamed Amine AouichaouiIn 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...
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Some new facts about linear maps that preserve the orthogonal group Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-09-20
M. Różański, R. Wituła, R. SłowikIn 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...
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Jordan derivations on Hilbert C*-modules Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-09-18
Huimin Chen, Xiaofei QiAssume 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...
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Bipartite unicyclic graphs with a unique perfect matching having the smallest positive eigenvalue equal to Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-09-18
Sasmita Barik, Subhasish Behera, Steve KirklandThe 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...
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The products of involutions in the centralizer of a Weyr matrix with nonhomogeneous Weyr structure Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-09-17
Ralph John L. de la Cruz, Raymond Louis S. TañedoA 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...
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Strong commutativity preserving maps on rank k strictly triangular matrices Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-09-16
Wai Leong Chooi, Chin Yie ChuaLet 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 ...
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Weighted generalized core–EP inverse Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-09-16
Dijana Mosić, Janko MarovtTo 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...
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On 2-local derivations of von Neumann algebras Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-09-11
Lei LiuLet 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...
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One sided star and core orthogonality of matrices Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-09-08
D. E. Ferreyra, F. E. Levis, Saroj B. Malik, R. P. MoasWe 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 ...
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Singularity of oriented tricyclic graphs Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-09-08
Xianya Geng, Mengxia Li, Xiaoxuan Chen, Long WangA 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...
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Affine phase retrieval of quaternion signals Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-08-29
Yun-Zhang Li, Ming YangQuaternion 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...
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Sharp lower bounds for the Laplacian Estrada index of graphs Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-08-27
Sasmita Barik, Tahir ShamsherLet 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 ...
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Correction of ‘J. Laderman, V. Pan, X.–H. Sha, On practical Algorithms for Accelerated Matrix Multiplication, Linear Algebra and its Applications. Vol. 162-164 (1992) pp. 557-588’ Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-08-19
Jerzy S. RespondekIn 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...
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(w,v)-core–EP inverse and (w,v)-pseudo-core inverse Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-08-15
Xavier Mary, Dijana Mosić, Huihui ZhuThe 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...
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Entries of the bottleneck matrices of maximal outerplanar graphs Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-08-05
Jason J. MolitiernoIn 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...
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The core-EP inverse: a numerical approach for its acute perturbation Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-08-05
Mengmeng Zhou, Jianlong Chen, Néstor ThomeThis 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...
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Global solutions of approximation problems in Krein spaces Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-08-02
M. ContinoThree 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...
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Laplacian eigenvalue distribution, diameter and domination number of trees Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-07-30
Jiaxin Guo, Jie Xue, Ruifang LiuFor 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 ...
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Additive decomposability preserving maps between exterior powers of vector spaces Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-07-23
Jinting Lau, Ming Huat LimIn 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...
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Constructing cospectral hypergraphs Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-07-25
Aida Abiad, Antonina P. KhramovaSpectral 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...
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Diameter of the BJ-orthograph in finite-dimensional C*-algebras Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-07-25
Srdjan StefanovićWe 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...
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On the signs of the principal minors of Hermitian matrices Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-07-19
Xavier Martínez-Rivera, Kamonchanok SaejeamThe 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...
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On the matrix Heinz means and Rényi divergences Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-07-16
Raluca Dumitru, Jose A. FrancoBhatia, 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...
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Approximating the closest structured singular matrix polynomial Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-07-09
Miryam Gnazzo, Nicola GuglielmiConsider 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...
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On the splitting iteration method for Pareto eigenvalue complementarity problems of H+-matrices Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-07-10
Lu Zou, Yuan LeiWe 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...
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An improvement and a generalization of Rotfel'd type inequalities for sectorial matrices Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-07-10
Fanghong Nan, Teng ZhangBy 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...
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On commutators of idempotents Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-07-06
Roman DrnovšekLet 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...
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Fredholm theory on Krein spaces and its application to pseudospectrum Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-07-06
Mohammed Zerai Dhahri, Aref Jeribi, Kamel MahfoudhiIn 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 ...
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The volume of an isocanted cube is a determinant* Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-07-03
M. J. de la Puente, P. L. ClaveríaIn 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
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Perturbation properties of the generalized spectral radius Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-06-18
Florian Bünger, Alberto SeegerLet 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∈...
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Correction Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-06-17
Published in Linear and Multilinear Algebra (Ahead of Print, 2024)
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2-local S mappings with respect to τ on some *-subalgebras of Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-06-05
Bing Yang, Chengjun Hou, Xiaochun FangWe 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...
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Linear operators and construction of symmetric symbols satisfying sum rules of order p Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-06-05
A. T. MithunWe 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...
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Quantum hitting time according to a given distribution Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-06-04
Paola Boito, G. M. Del CorsoIn 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 ...
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Maximal border subrank tensors Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-05-27
Chia-Yu ChangWe prove a lower bound on the dimension of the set of maximal border subrank tensors. This is the first such bound of its type.
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On affine spaces of alternating matrices with constant rank Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-05-20
Clément de Seguins PazzisLet 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...
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Optimization of some types of Rényi divergences between unitary orbits Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-05-20
Cong Trinh Le, The Khoi Vu, Minh Toan Ho, Trung Hoa DinhIn 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...
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Grothendieck-type characterization of representable multilinear mappings Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-05-14
Raffaella Cilia, Joaquín M. GutiérrezLet 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...
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The parallel sum in C*-algebras Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-05-13
Ali Zamani, Hasan Karimi, Qingxiang XuLet 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 ...
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On simple evolution algebras of dimension two and three. Constructing simple and semisimple evolution algebras Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-05-13
Yolanda Cabrera Casado, Dolores Martín Barquero, Cándido Martín González, Alicia TocinoThis 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, ...
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Characterization and construction of sign regular tridiagonal matrices Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-05-09
P. Abascal, F. Fueyo, J. Jimenez, A. Palacio, M. L. SerranoIn 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...
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Nice operators and nice spaces Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-05-08
Sasan Amiri, Azin Golbaharan, Hakimeh MahyarIn 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...
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The CPO-inverse and its partial orders Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-05-07
Ju Gao, Hongxing Wang, Shuangzhe LiuThis 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...
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Extremal marginals of an unbounded local completely positive and local completely contractive map Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-05-07
Maria JoiţaIn 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 ...
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Refined von Neumann-type trace inequality and its application Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-05-05
Yazhou Han, Cheng Yan, Xingpeng ZhaoThe 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...
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Procrustes problem for the inverse eigenvalue problem of normal (skew) J-Hamiltonian matrices and normal J-symplectic matrices Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-05-05
S. Gigola, L. Lebtahi, N. ThomeA 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...
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Upper bounds for the norm of the sum and Kronecker product of Hilbert space operators Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-04-29
Mohammad Sababheh, Hamid Reza Moradi, Mario KrnićThis 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...