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A certain decomposition of infinite invertible matrices over division algebras Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-06-27 Mai Hoang Bien, Truong Huu Dung, Nguyen Thi Thai Ha
Let D be an infinite division ring with centre F and T(∞,D) the group of infinite upper triangular invertible matrices indexed by N×N over D. In this paper, we first show that if D is finite dimensional over F, then every element in T(∞,D) whose diagonal entries are commutators of D∖{0} is a commutator of an infinite diagonal matrix and another infinite upper triangular matrix. Some applications are
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New unitary equivalences for some operator matrices with applications Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-06-25 O. Abdollahi, S. Karami, J. Rooin
In this paper, first we consider cross-diagonal, in particular off-diagonal, operator matrices; those operator matrices such that all entries except those on the main and off diagonals are zero. We show that this operator matrix is unitarily equivalent to a block diagonal operator matrix whose diagonal blocks are all two-by-two, except at most one of them which is one-by-one. Then, using this unitary
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A direct method for the simultaneous updating of finite element mass, damping and stiffness matrices Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-06-25 Jiajie Luo, Lina Liu, Sisi Li, Yongxin Yuan
This paper is mainly concerned with a model updating problem for damped structural systems, which can be described as the following inverse quadratic eigenvalue problem (IQEP) and an optimal approximate problem (OAP). Problem IQEP: Given matrices Λ=diag{λ1,…,λp}∈Cp×p and X=[x1,…,xp]∈Cn×p with p≤n, λi≠λj for i≠j, i,j=1,…,p, rank(X)=p and both Λ and X being closed under complex conjugation, find real
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On the Hadamard product A A, for a singular M-matrix A Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-06-25 Manami Chatterjee, K.C. Sivakumar
The problem of determining lower bounds for the second and numerically smallest eigenvalue of A∘A#, when A is a group invertible singular M-matrix, is considered.
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A strict inequality on the energy of edge partitioning of graphs Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-06-25 Saieed Akbari, Kasra Masoudi, Sina Kalantarzadeh
Let G be a graph. The energy of G, E(G), is defined as the sum of absolute values of its eigenvalues. Here, it is shown that if G is a graph and {H1,…,Hk} is an edge partition of G, such that H1,…,Hk are spanning; then E(G)=∑i=1kE(Hi) if and only if AiAj=0, for every 1⩽i,j⩽k and i≠j, where Ai is the adjacency matrix of Hi. It was proved that if G is a graph and H1,…,Hk are subgraphs of G which partition
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GIBS: a general and efficient iterative method for computing the approximate inverse and Moore–Penrose inverse of sparse matrices based on the Schultz iterative method with applications Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-06-25 Eisa Khosravi Dehdezi, Saeed Karimi
In this paper, an algorithm is proposed to compute the inverse of an invertible matrix. The new algorithm is a generalization of the algorithms based on the well-known Schultz-type iterative methods. We show that the convergence order of the new method is a linear combination of the Fibonacci sequence and also is powerful and efficient in finding and keeping sparsity of the obtained approximate inverse
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Norm inequalities for positive definite matrices related to a question of Bourin Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-06-22 Amer Darweesh, Mostafa Hayajneh, Saja Hayajneh, Fuad Kittaneh
Let A and B be positive definite matrices of the same size, and let α≥1. If the spectrum of AB−1 lies in the interval [1,α], then |||AtB1−t+BtA1−t|||≤α|||A+B|||for t∈[0,1] and for every unitarily invariant norm. This norm inequality is closely related to an open question of Bourin.
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Scaffoldings of totally positive matrices and line insertion Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-06-17 Karel Casteels
Given a totally positive matrix, can one insert a line (row or column) between two given lines while maintaining total positivity? This question was first posed and solved by Johnson and Smith who gave an algorithm that results in one possible line insertion. In this work, we revisit this problem. First, we show that every totally positive matrix can be associated with a certain vertex-weighted graph
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Asymptotic distribution of resonances for matrix Schrödinger operator in one dimension Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-06-10 Salmine Abdelmoula, Hamadi baklouti
Using some classical theorems on entire functions, we determine the asymptotic for the counting function of the resonances for 2×2 matrix Schrödinger operator in one dimension for potentials with compact support.
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A new almost convergent sequence space defined by Schröder matrix Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-06-10 Muhammet Cihat Dağli
This paper deals with a new almost convergent sequence space constructed by Schröder matrix. It is shown that this new sequence space is linearly isomorphic to the space of all almost convergent sequences. Also, the β-dual of the resulting space is expressed and Schröder core of a complex-valued sequence is introduced. Moreover, some inclusion theorems are obtained for this new type of core.
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Hankel determinant of linear combination of the shifted catalan numbers Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-06-03 Habib Rebei, Anis Riahi, Wathek Chammam
In this paper, we give a method for the evaluation of Hankel determinant of a linear combination of Catalan numbers. Then, we extend this result to shifted Catalan numbers. This is done by finding a Jacobi linear functional, such that their moments are the Catalan numbers or the shifted Catalan numbers. The values of such determinants are then expressed in terms of Jacobi polynomials.
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Bounds for the Perron root of positive matrices Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-06-02 Ping Liao
New bounds for the Perron root ρ(A) of a positive matrix A are proposed. Let R1≥R2≥⋯≥Rn be the row sums of matrix A listed in descending order. We use a pairwise combination method to prove that min1≤k≤j{(1−t)Rk+tRn−k+1}≤ρ(A)≤max1≤k≤j{tRk+(1−t)Rn−k+1},with j=⌈n/2⌉, t=M/(M+m), and M (respectively m) is the maximum (resp. minimum) entry of A. This result improves the well-known bounds Rn≤ρ(A)≤R1, and
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On the Davis–Wielandt radius inequalities of Hilbert space operators Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-27 M. W. Alomari
In this work, some new upper and lower bounds for the Davis–Wielandt radius are introduced. Generalizations of some presented results are obtained. Some bounds for the Davis–Wielandt radius for n×n operator matrices are established. An extension of the Davis–Wielandt radius to the Euclidean operator radius is introduced.
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Matchings in graphs from the spectral radius Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-18 Minjae Kim, Suil O, Wooyong Sim, Dongwoo Shin
The matching number of G, written α′(G), is the size of a maximum matching in G. Suppose that n and k are positive integers of the same parity. Let θ′(n,k) be the largest root of x3−(n−k−2)x2−(n−1)x+k(n−k−2)=0 and θ(n,k)={θ′(n,k)ifn≥3k+2n−k−2+(n−k−2)2+4(n2−k2)4ifn≤3k.In this article, we prove that for a positive integer n≥k+2, if G is an n-vertex connected graph with the spectral radius ρ(G)>θ(n,k)
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An analogue of the relationship between SVD and pseudoinverse over double-complex matrices Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-18 Ran Gutin
We present a generalization of the pseudoinverse operation to pairs of matrices, as opposed to single matrices alone. We note the fact that the Singular Value Decomposition can be used to compute the ordinary Moore-Penrose pseudoinverse. We present an analogue of the Singular Value Decomposition for pairs of matrices, which we show is inadequate for our purposes. We then present a more sophisticated
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Formulas for the eigendiscriminants of ternary and quaternary forms Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-16 Laurent Busé
A d-dimensional tensor A of format n×n×⋯×n defines naturally a rational map Ψ from the projective space Pn−1 to itself and its eigenscheme is then the subscheme of Pn−1 of fixed points of Ψ. The eigendiscriminant is an irreducible polynomial in the coefficients of A that vanishes for a given tensor if and only if its eigenscheme is singular. In this paper, we contribute two formulas for the computation
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New views of the doubly stochastic single eigenvalue problem Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-14 Charles Johnson, Stephen Newman, Ilya Spitkovsky
The question of which elements of the open unit disc occur as eigenvalues of n-by-n doubly stochastic matrices has long been open, in spite of a number of intriguing partial results. By enhancing a natural, but slightly false, conjecture, we gain some new computational insights into the problem. We also apply the classical field of values to give some partial results on both the necessity of certain
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Quadratic realizability of palindromic matrix polynomials: the real case Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-13 Vasilije Perović, D. Steven Mackey
Let L=(L1,L2) be a list consisting of structural data for a matrix polynomial; here L1 is a sublist consisting of powers of irreducible (monic) scalar polynomials over the field R, and L2 is a sublist of nonnegative integers. For an arbitrary such L, we give easy-to-check necessary and sufficient conditions for L to be the list of elementary divisors and minimal indices of some real T-palindromic quadratic
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The Jordan and Frobenius pairs of the inverse Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-13 Enrico Bozzo, Piero Deidda, Carmine Di Fiore
Given a matrix A∈Cn×n there exists a nonsingular matrix V such that V−1AV=J, where J is a very sparse matrix with a diagonal block structure, known as the Jordan canonical form (JCF) of A. Assume that A is nonsingular and that V and J are given. How to obtain V^ and J^ such that V^−1A−1V^=J^ and J^ is the JCF of A−1? Curiously, the answer involves the Pascal matrix. For the Frobenius canonical form
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On the lengths of matrix incidence algebras with radicals of square zero Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-12 N. A. Kolegov
The lengths of matrix incidence algebras are studied when their radicals have square zero. All realizable values of the length function are provided for such algebras. In order to obtain this result, a discrete optimization problem is posed and solved. Also, the exact formula of the length is deduced under the additional assumption that the algebra is maximal by inclusion. Moreover, the solution to
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Visualization for Petrov's odd unitary group Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-09 A. A. Ambily, V. K. Aparna Pradeep
In this article, we define a set of matrices analogous to Vaserstein-type matrices, which were introduced in the paper ‘Serre's problem on projective modules over polynomial rings and algebraic K-theory’ by Suslin–Vaserstein in 1976. We prove that these are elementary linear matrices. Also, under some conditions, these matrices belong to Petrov's odd unitary group, which is a generalization of all
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The maximum principal ratio of graphs Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-07 Lele Liu, Changxiang He
Let G be a connected graph. The principal ratio of G is the ratio of the maximum and minimum entries of its Perron eigenvector. In 2007, Cioabă and Gregory conjectured that among all connected graphs on n vertices, the kite graph attains the maximum principal ratio. In 2018, Tait and Tobin confirmed the conjecture for sufficiently large n. In this article, we show the conjecture is true for all n≥5000
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Rational matrix digit systems Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-07 Jonas Jankauskas, Jörg M. Thuswaldner
Let A be a d×d matrix with rational entries which has no eigenvalue λ∈C of absolute value |λ|<1 and let Zd[A] be the smallest nontrivial A-invariant Z-module. We lay down a theoretical framework for the construction of digit systems (A,D), where D⊂Zd[A] finite, that admit finite expansions of the form x=d0+Ad1+⋯+Aℓ−1dℓ−1(ℓ∈N,d0,…,dℓ−1∈D)for every element x∈Zd[A]. We put special emphasis on the explicit
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Intermixing pairs of generalized inverses Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-07 Michael P. Drazin
It is shown that, in any semigroup with involution, both the DMP inverse of Malik and Thome [Appl Math Comp. 2014;226:575–580.] and the CMP inverse of Mehdipour and Salemi [Linear Multilinear Alg. 2018;66:1046–1053.] are special cases of the Bott–Duffin (e,f)-inverse introduced in [Linear Algebra Appl. 2012;436:1909-1923.] It is also shown that the core inverse of O.M. Baksalary and Trenkler [Linear
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A generalized Wigner–Yanase skew information Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-07 Rupinderjit Kaur Dhanoa, Mohammad Sal Moslehian, Mandeep Singh
We generalize a two-parameter extended Wigner–Yanase skew information given by Z. Zhang [J Math Anal Appl. 2021;497(1): 124851] to any general operator monotone function. We prove several fundamental properties including the joint concavity and an uncertainty relation for the proposed generalized Wigner–Yanase skew information.
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On the maximal α-spectral radius of graphs with given matching number Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-04 Xiying Yuan, Zhenan Shao
Let Gn,β be the set of graphs of order n with given matching number β. Let D(G) be the diagonal matrix of the degrees of the graph G and A(G) be the adjacency matrix of the graph G. The largest eigenvalue of the nonnegative matrix Aα(G)=αD(G)+A(G) is called the α-spectral radius of G. The graphs with maximal α-spectral radius in Gn,β are completely characterized in this paper. In this way, we provide
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Extremal realization spectra by two acyclic matrices whose graphs are caterpillars Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-05-02 S. Arela-Pérez, J. Egaña, G. Pastén, H. Pickmann-Soto
This paper studies two inverse eigenvalue problems for two kinds of acyclic matrices whose graphs are caterpillars. The spectral data of the first problem considers the minimal and maximal eigenvalues of all leading principal submatrices of the matrix. The second consists of an extremal eigenvalue of each leading principal submatrix and one eigenpair of the matrix. In the main results, we give sufficient
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Moment of a subspace and joint numerical range Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-28 Abel H. Klobouk, Alejandro Varela
For a subspace S of Cn and a fixed basis, we study the compact and convex set mS=convexhull {|s|2∈R≥0n:s∈S and ‖s‖=1}≃{Diag(Y)∈Mnh(C):Y≥0,tr(Y)=1,PSYPS=Y}that we call the moment of S, where |s|2=(|s1|2,|s2|2,…,|sn|2). This set is relevant in the determination of minimal hermitian matrices ( M∈Mnh such that ‖M+D‖≤D for every diagonal D and the spectral norm ‖⋅‖). We describe extremal points and certain
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A modified generalized SOR-like method for solving an absolute value equation Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-27 Jia-Lin Zhang, Guo-Feng Zhang, Zhao-Zheng Liang
In this paper, we propose a modified generalized SOR-like (MGSOR) method for solving an absolute value equation (AVE), which is obtained by reformulating equivalently AVE as a two-by-two block nonlinear equation and by introducing the transformation Py:=|x| with a general nonsingular matrix P. The convergence results of the MGSOR method are obtained under certain assumptions imposed on the involved
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A representation of compact C-normal operators Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-28 G. Ramesh, B. Sudip Ranjan, D. Venku Naidu
Let C be a conjugation on a complex separable Hilbert space H. A bounded linear operator T is said to be C-normal if CT∗TC=TT∗. In this paper, first, we give a representation of C-normal operators on finite dimensional Hilbert space and later extend it to compact C-normal operators on infinite-dimensional separable Hilbert spaces. In the end, we discuss the eigenvalue problem for C-normal operators
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Some properties of c-K-g-frames in Hilbert C*-modules Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-27 Javad Baradaran, Jahangir Cheshmavar, Fereshte Nikahd, Zahra Ghorbani
A number of differences exist between the structures of Hilbert spaces and Hilbert C∗-modules. This work aims at studying some properties and characterizations of c-K-g-frames in Hilbert C∗-modules. Moreover, the dual c-K-g-Bessel system for a given c-K-g-frame in a Hilbert C∗-module is introduced and all dual c-K-g-Bessel systems are characterized. Finally, we provide sufficient conditions under which
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(A, m)-partial isometries in semi-Hilbertian spaces Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-27 Adel Saddi, Fatma Mahmoudi
In this paper, we introduce the notion of (A,m)-partial isometry for a positive operator A and a nonnegative integer m. This family of operators contains both the class of (A,m)-isometries discussed in Sid Ahmed and Saddi [A-m-isometric operators in semi-Hilbertian spaces. Linear Algebra Appl. 2012;436:3930–3942] and that of m-partial isometries introduced in Saddi and Sid Ahmed [m-partial isometries
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Contractive symmetric matrix completion problems related to graphs Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-22 Sangmin Chun, In Hyoun Kim, Jaewoong Kim, Jasang Yoon
In this paper, we consider the contractive real symmetric matrix completion problems motivated in part by studies on sparse (or dense) matrices for weighted sparse recovery problems and rating matrices with rating density in recommender systems. We completely characterize symmetric patterns P with the property (C) that every partially contractive real symmetric matrix with pattern P has a contractive
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Inertia indices of a complex unit gain graph in terms of matching number Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-20 Qi Wu, Yong Lu
A complex unit gain graph is a triple Φ=(G,T,φ) (or Gφ for short) consisting of a simple graph G, as the underlying graph of Gφ, the set of unit complex numbers T={z∈C:|z|=1} and a gain function φ:E→→T such that φ(ei,j)=φ(ej,i)−1. Let A(Gφ) be the adjacency matrix of Gφ. In this paper, we prove that m(G)−c(G)≤p(Gφ)≤m(G)+c(G),m(G)−c(G)≤n(Gφ)≤m(G)+c(G),where p(Gφ), n(Gφ), m(G) and c(G) are the number
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On analytic structure of weighted shifts on generalized directed semi-trees Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-20 Gargi Ghosh, Somnath Hazra
Inspired by natural classes of examples, we define generalized directed semi-trees and construct weighted shifts on them. Given an n-tuple of generalized directed semi-trees with certain properties, we associate an n-tuple of multiplication operators on a Hilbert space H2(β) of formal power series. Under certain conditions, H2(β) turns out to be a reproducing kernel Hilbert space consisting of holomorphic
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Classification of involutive automorphisms and anti-automorphisms of the Lie algebra of quaternions Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-19 Jimmie Lawson, Eyüp Kizil
In this article, we treat the space H of real quaternions as a Lie algebra equipped with its commutator product. We show that all involutions of this Lie algebra that are automorphisms (respectively, anti-automorphisms) and restrict to the identity on the centre R⋅1 (sometimes called automorphisms of the first kind) are actually algebra automorphisms (resp. anti-automorphisms) of the division algebra
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Minimality of tensors of fixed multilinear rank Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-19 Alexander Heaton, Khazhgali Kozhasov, Lorenzo venturello
We discover a geometric property of the space of tensors of fixed multilinear (Tucker) rank. Namely, it is shown that real tensors of the fixed multilinear rank form a minimal submanifold of the Euclidean space of tensors endowed with the Frobenius inner product. We also establish the absence of local extrema for linear functionals restricted to the submanifold of rank-one tensors, finding application
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Modified block product preconditioner for a class of complex symmetric linear systems Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-18 Fariba Bakrani Balani, Masoud Hajarian
This paper introduces a modified block product preconditioner for a class of complex symmetric linear systems which is constructed by the equivalent real block two-by-two structure of the coefficient matrix. We discuss the convergence of the associated iterative method and determine the optimal choice of the iteration parameter. Furthermore, some algebraic properties of the preconditioned matrix are
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Spaces of generators for matrix algebras with involution Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-18 Taeuk Nam, Cindy Tan, Ben Williams
Let k be an algebraically closed field of characteristic different from 2. Up to isomorphism, the algebra Matn×n(k) can be endowed with a k-linear involution in one way if n is odd and in two ways if n is even. In this paper, we consider r-tuples A∙∈Matn×n(k)r such that the entries of A∙ fail to generate Matn×n(k) as an algebra with involution. We show that the locus of such r-tuples forms a closed
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An equation concerning power values of generalized skew derivations and annihilating conditions on Lie ideals Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-18 Vincenzo De Filippis, Giovanni Scudo
Let R be a prime ring of characteristic different from 2, Qr its right Martindale quotient ring and C its extended centroid. Suppose that F is a generalized skew derivation of R, L a non-central Lie ideal of R, a∈R a non-zero element of R, m,r≥1 and s,t≥0 fixed integers. If a(F(u)r(F(u)su+uF(u)s)F(u)t)m=0 for all u∈L, then either there exists b∈Qr such that F(x)=bx, for any x∈R, with ab = 0 or R⊆M2(K)
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On unicyclic non-bipartite graphs with tricyclic inverses Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-18 Debajit Kalita, Kuldeep Sarma
The class of unicyclic non-bipartite graphs with unique perfect matching, denoted by U, is considered in this article. This article provides a complete characterization of unicyclic graphs in U which possess tricyclic inverses.
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Derivations of triangular matrix rings Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-18 D. I. Vladeva
In this paper, the author gives a description of the derivations of UTMn(R), the ring of upper triangular matrices over an associative ring R with identity. The main result states that if D is an arbitrary derivation of the ring UTMn(R) and A∈UTMn(R), then there are matrices, such that the derivative D(A) is a linear combination of the values of well-known derivations of these matrices.
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Operator geodesically convex functions and their applications Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-13 Venus Kaleibary, Mohammad Reza Jabbarzadeh, Shigeru Furuichi
In this paper, we introduce operator geodesically convex and operator convex-log functions and characterize some properties of them. Then we apply these classes of functions to present several operator Azcél and Minkowski-type inequalities extending some known results. The concavity counterparts are also considered.
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A novel conservative matrix arising from Schröder numbers and its properties Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-12 Muhammet Cihat Dağli
In this paper, we introduce a new conservative matrix involving Schröder numbers and investigate its matrix domain in the sequence spaces c and c0. Furthermore, the Köthe–Toeplitz dual, generalized Köthe–Toeplitz dual and Garling dual are expressed and several matrix transformations are given based on the new Banach spaces.
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Common properties among various generalized inverses and constrained binary relations Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-12 Ruifei Kuang, Chunyuan Deng
The common characterizations and various individual properties of different generalized inverses are established. Several equivalent conditions for the core-EP, weak group inverse, m-weak group inverse and weak core inverse are presented. The brand new explicit expressions for the operator binary relations defined by various generalized inverses are obtained. We derive properties and study the relationship
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Von Neumann regular matrices revisited Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-07 Iulia-Elena Chiru, Septimiu Crivei
We give a constructive sufficient condition for a matrix over a commutative ring to be von Neumann regular, and we show that it is also necessary over local rings. Specifically, we prove that a matrix A over a local commutative ring is von Neumann regular if and only if A has an invertible ρ(A)×ρ(A)-submatrix if and only if the determinantal rank ρ(A) and the McCoy rank of A coincide. We deduce consequences
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A note on -gradings on the Grassmann algebra and elementary number theory Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-07 Claudemir Fidelis, Alan Guimarães, Plamen Koshlukov
Let E be the Grassmann algebra of an infinite-dimensional vector space L over a field of characteristic zero. In this paper, we study the Z-gradings on E having the form E=E(r1,r2,r3)(v1,v2,v3), in which each element of a basis of L has Z-degree r1,r2, or r3. We provide a criterion for the support of this structure to coincide with a subgroup of the group Z, and we describe the graded identities for
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On an integral representation of the normalized trace of the k-th symmetric tensor power of matrices and some applications Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-05 Hassan Issa,Hassane Abbas,Bassam Mourad
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New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-05 Mohammad M. Ghabries, Hassane Abbas, Bassam Mourad, Abdallah Assi
The purpose of this paper is to establish new log-majorization results concerning eigenvalues and singular values which generalize some previous work related to a conjecture and an open question which were presented by Lemos and Soares in 2018. In addition, we present a complement of a unitarily invariant norm inequality which was conjectured by Bhatia, Lim and Yamazaki in 2016, and recently proved
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Weighted Jordan homomorphisms Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-04-05 M. Brešar, M. L. C. Godoy
Let A and B be unital rings. An additive map T:A→B is called a weighted Jordan homomorphism if c=T(1) is an invertible central element and cT(x2)=T(x)2 for all x∈A. We provide assumptions, which are in particular fulfilled when A=B=Mn(R) with n≥2 and R any unital ring with 12, under which every surjective additive map T:A→B with the property that T(x)T(y)+T(y)T(x)=0 whenever xy = yx = 0 is a weighted
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CFI upper triangular operator matrices Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-03-31 Jiong Dong, Xiaohong Cao
Let H and K be complex infinite dimensional separable Hilbert spaces. For given operators A∈B(H) and B∈B(K), we provide necessary and sufficient conditions which make a 2×2 upper triangular operator matrix MC=(AC0B) a CFI operator for some (or every) C∈B(K,H).
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Conditions for matchability in groups and field extensions Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-03-31 Mohsen Aliabadi, Jack Kinseth, Christopher Kunz, Haris Serdarevic, Cole Willis
The origins of the notion of matchings in groups spawn from a linear algebra problem proposed by E. K. Wakeford [On canonical forms. Proc London Math Soc (2). 1920;18:403–410] which was tackled in Fan and Losonczy [Matchings and canonical forms for symmetric tensors. Adv Math. 1996;117(2):228–238]. In this paper, we first discuss unmatchable subsets in abelian groups. Then we formulate and prove linear
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Davis-Wielandt radius inequalities for off-diagonal operator matrices Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-03-29 Xiaomei Dong, Deyu Wu
In this paper, we generalize several inequalities involving powers of the Davis-Wielandt radius for off-diagonal part of 2×2 operator matrices of the form T=(0BC0), where B and C are two bounded linear operators. We also obtain some new upper and lower bounds for the Davis-Wielandt radius of bounded linear operators, which generalize the existing ones.
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Poisson triple systems Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-03-24 Murray R. Bremner, Hader A. Elgendy
We introduce Poisson triple systems, which are vector spaces with 3 trilinear operations satisfying 9 polynomial identities of degree 5. We show that every Poisson triple system has a universal enveloping Poisson algebra. Finally, we briefly discuss operadic aspects of Poisson triple systems.
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On the description of identifiable quartics Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-03-19 Elena Angelini, Luca Chiantini
ABSTRACT In this paper, we study the identifiability of specific forms (symmetric tensors), with the target of extending recent methods for the case of 3 variables to more general cases. In particular, we focus on forms of degree 4 in 5 variables. By means of tools coming from classical algebraic geometry, such as Hilbert function, liaison procedure and Serre's construction, we give a complete geometric
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Some numerical radius inequality for several semi-Hilbert space operators Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-03-19 Cristian Conde, Kais Feki
The paper deals with the generalized numerical radius of linear operators acting on a complex Hilbert space H, which are bounded with respect to the seminorm induced by a positive operator A on H. Here A is not assumed to be invertible. Mainly, if we denote by ωA(⋅) and ω(⋅) the generalized and the classical numerical radii respectively, we prove that for every A-bounded operator T we have ωA(T)=ω(A1/2T(A1/2)†)
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Determinants in Jordan matrix algebras Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-03-19 Jan Hamhalter, Ondřej F.K. Kalenda, Antonio M. Peralta
We introduce a natural notion of determinants in matrix JB ∗-algebras, i.e. for hermitian matrices of biquaternions and for hermitian 3×3 matrices of complex octonions. We establish several properties of these determinants which are useful to understand the structure of the Cartan factor of type 6. As a tool, we provide an explicit description of minimal projections in the Cartan factor of type 6 and
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The Aα-spectral radius of dense graphs Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-03-19 Muhuo Liu, Chaohui Chen, Shu-Guang Guo, Jiarong Peng, Tianyuan Chen
A c-cyclic graph is a connected graph with n vertices and n + c−1 edges. In this paper, we consider the problem that: in the class of graphs, each of which is the complement graph of a c-cyclic graph with n vertices, which graph has the largest Aα-spectral radius. We shall show that, for 0≤c≤n−4, the extremal graph must be a graph with an isolated vertex. This implies that the maximum degree of G is
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The minimum number of multiplicity 1 eigenvalues among real symmetric matrices whose graph is a 2-linear tree Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-03-19 Wenxuan Ding, Matthew Ingwersen, Charles R. Johnson
For a tree T, U(T) denotes the minimum number of eigenvalues of multiplicity 1 among all real symmetric matrices, whose graph is T. It is known that U(T)≥2. A tree is linear if all its vertices of degree at least 3 lie on a single induced path, and k-linear if there are k of these high degree vertices. U(T) is known for generalized stars (1-linear trees), and U(T) is determined here for 2-linear trees
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A commutative algebra approach to multiplicative Hom-Lie algebras Linear Multilinear Algebra (IF 1.736) Pub Date : 2022-03-17 Yin Chen, Runxuan Zhang
Let g be a finite-dimensional complex Lie algebra and HLiem(g) be the affine variety of all multiplicative Hom-Lie algebras on g. We use a method of computational ideal theory to describe HLiem(gln(C)), showing that HLiem(gl2(C)) consists of two 1-dimensional and one 3-dimensional irreducible components and HLiem(gln(C))={diag{δ,…,δ,a}∣δ=1or0,a∈C} for n⩾3. We construct a new family of multiplicative