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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 Guglielmi
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...
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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 Lei
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...
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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 Zhang
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...
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On commutators of idempotents Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-07-06 Roman Drnovšek
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...
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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 Mahfoudhi
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 ...
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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. Clavería
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
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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 Seeger
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∈...
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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 Fang
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...
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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. Mithun
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...
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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 Corso
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 ...
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Maximal border subrank tensors Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-05-27 Chia-Yu Chang
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.
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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 Pazzis
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...
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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 Dinh
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...
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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. Gutiérrez
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...
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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 Xu
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 ...
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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 Tocino
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, ...
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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. Serrano
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...
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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 Mahyar
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...
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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 Liu
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...
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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 Joiţa
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 ...
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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 Zhao
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...
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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. Thome
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...
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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 Krnić
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...
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Non-exposed polyhedral faces of the completely positive cone Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-04-29 O. I. Kostyukova
In this paper, we consider the cone of p×p completely positive matrices CP(p). Currently, some families of non-exposed faces of the 5×5 completely positive cone CP(5) were constructed. Inspired by ...
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On eigenvalues of certain special matrices Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-04-29 Manisha Devi, Jaspal Singh Aujla
Let g:R→[0,∞) be a conditionally negative definite function and f:[0,∞)→[0,∞) be a Bernstein function. We prove that the function h=f∘g is conditionally negative definite and that for distinct real...
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Deflating subspaces of T-palindromic pencils and algebraic T-Riccati equations Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-04-22 Bruno Iannazzo, Beatrice Meini, Federico Poloni
By exploiting the connection between solving algebraic ⊤-Riccati equations and computing certain deflating subspaces of ⊤-palindromic matrix pencils, we obtain theoretical and computational results...
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Very good gradings on matrix rings are epsilon-strong Linear Multilinear Algebra (IF 0.9) Pub Date : 2024-04-22 Patrik Lundström, Johan Öinert, Laura Orozco, Héctor Pinedo
We investigate properties of group gradings on matrix rings Mn(R), where R is an associative unital ring and n is a positive integer. More precisely, we introduce very good gradings and show that a...
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Strictly monotone sequences of lower and upper bounds on Perron values and their combinatorial applications Linear Multilinear Algebra (IF 0.9) 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...
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Fixed point groups of involutions of type O(q,k) over a field of characteristic two Linear Multilinear Algebra (IF 0.9) 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...
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Computing a compact local Smith–McMillan form Linear Multilinear Algebra (IF 0.9) 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...
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Generalized matricial ranges and positive definiteness Linear Multilinear Algebra (IF 0.9) 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...
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A novel structure-preserving algorithm for the singular value decomposition of biquaternion matrices Linear Multilinear Algebra (IF 0.9) 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...
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VDR decomposition of Chebyshev-Vandermonde matrices with the Arnoldi Process Linear Multilinear Algebra (IF 0.9) 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...
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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 0.9) 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...
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Ordering of graphs with fixed size and diameter by Aα-spectral radii Linear Multilinear Algebra (IF 0.9) 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...
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The kernels of powers of linear operator via Weyr characteristic Linear Multilinear Algebra (IF 0.9) 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...
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The Jordan algebraic structure of the rotated quadratic cone Linear Multilinear Algebra (IF 0.9) 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...
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Generalizing Choi map in M3 beyond circulant scenario Linear Multilinear Algebra (IF 0.9) 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...
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Modified CRI iteration methods for complex symmetric indefinite linear systems Linear Multilinear Algebra (IF 0.9) 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...
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On an analogue of a property of singular M-matrices for the Lyapunov and Stein operators Linear Multilinear Algebra (IF 0.9) 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...
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Countably many asymptotic tensor ranks Linear Multilinear Algebra (IF 0.9) 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...
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Rank one quaternionic operators and additive preservers Linear Multilinear Algebra (IF 0.9) 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...
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Lie triple centralizers of the algebra of dominant block upper triangular matrices Linear Multilinear Algebra (IF 0.9) 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...
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Distance spectral radius and fractional matching in t-connected graphs Linear Multilinear Algebra (IF 0.9) 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...
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Probabilistic bounds on best rank-1 approximation ratio Linear Multilinear Algebra (IF 0.9) 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...
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A note on a generalized Jordan form of an infinite upper triangular matrix Linear Multilinear Algebra (IF 0.9) 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...
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Existence and uniqueness of solutions for Leontief's Input–Output Model, graph theory and sensitivity analysis Linear Multilinear Algebra (IF 0.9) 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, ...
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G-Drazin inverse combined with inner inverse Linear Multilinear Algebra (IF 0.9) 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...
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Minimizers for the energy of eccentricity matrices of trees Linear Multilinear Algebra (IF 0.9) 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...
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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 0.9) 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...
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Independence and orthogonality of algebraic eigenvectors over the max-plus algebra Linear Multilinear Algebra (IF 0.9) 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...
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Symmetric Hamiltonian vector fields Linear Multilinear Algebra (IF 0.9) 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 ...
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Unitary equivalences for k-circulant operator matrices with applications Linear Multilinear Algebra (IF 0.9) 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...
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Characterizing matrices with eigenvalues in an LMI region: a dissipative-Hamiltonian approach Linear Multilinear Algebra (IF 0.9) 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...
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Inner product inequalities with applications Linear Multilinear Algebra (IF 0.9) 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...
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Divisibility among power matrices associated with multiplicative functions Linear Multilinear Algebra (IF 0.9) 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
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Characterization of self-adjoint domains for regular odd order C-symmetric differential operators Linear Multilinear Algebra (IF 0.9) 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 ...
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The generalized sectorial decompositions of semi-sectorial operators Linear Multilinear Algebra (IF 0.9) 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...
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Forms of biisometric operators and biorthogonality Linear Multilinear Algebra (IF 0.9) 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...