Linear Algebra and its Applications最新文献

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Error estimates and higher order Trotter product formulas in Jordan-Banach algebras Jordan-Banach代数中的误差估计和高阶Trotter积公式

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2025-10-29 DOI: 10.1016/j.laa.2025.10.032

Sarah Chehade , Andrea Delgado , Shuzhou Wang , Zhenhua Wang

In quantum computing, Trotter estimates are critical for enabling efficient simulation of quantum systems and quantum dynamics, help implement complex quantum algorithms, and provide a systematic way to control approximate errors. In this paper, we extend the analysis of Trotter-Suzuki approximations, including third and higher orders, to Jordan-Banach algebras. We solve an open problem in our earlier paper on the existence of second-order Trotter formula error estimation in Jordan-Banach algebras. To illustrate our work, we apply our formula to simulate Trotter-factorized spins, and show improvements in the approximations. Our approach demonstrates the adaptability of Trotter product formulas and estimates to non-associative settings, which offers new insights into the applications of Jordan algebra theory to operator dynamics.

在量子计算中，Trotter估计对于实现量子系统和量子动力学的有效模拟至关重要，有助于实现复杂的量子算法，并提供系统的方法来控制近似误差。在本文中，我们将Trotter-Suzuki逼近的分析，包括三阶和高阶，推广到Jordan-Banach代数。我们解决了Jordan-Banach代数中二阶Trotter公式误差估计的存在性问题。为了说明我们的工作，我们应用我们的公式来模拟快步因子自旋，并显示了近似值的改进。我们的方法证明了Trotter乘积公式和估计对非联想设置的适应性，这为Jordan代数理论在算子动力学中的应用提供了新的见解。

引用次数: 0

Corrigendum to “Nilpotent linear spaces and Albert's Problem” [Linear Algebra Appl. 518 (2017) 57–78] “幂零线性空间与阿尔伯特问题”的勘误表[线性代数应用，518 (2017):57-78]

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2025-10-28 DOI: 10.1016/j.laa.2025.10.010

Juan C. Gutierrez Fernandez , E.O. Quintero Vanegas

In our article Nilpotent Linear Spaces and Albert's Problem [Linear Algebra Appl. 518 (2017) 57–78], the proof of Theorem 6 was incomplete, as a case was omitted. Here we supply the missing argument. The statement of Theorem 6, and all subsequent results depending on it, remain valid.

在我们的文章《幂零线性空间与阿尔伯特问题》[线性代数应用，518(2017)57-78]中，定理6的证明是不完整的，因为省略了一个情况。在这里，我们提供缺失的论据。定理6的陈述，以及所有依赖于它的后续结果，仍然有效。

引用次数: 0

Non-linear maps preserving ascent or descent of product of operators 保持运算符乘积上升或下降的非线性映射

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2025-10-27 DOI: 10.1016/j.laa.2025.10.026

Rabi Marzouki, Khalid Souilah

In this article, we provide a complete description of all maps on the algebra of all bounded linear operators acting on an infinite-dimensional complex Banach space, that leave invariant the ascent, or descent, under the product of two operators.

在这篇文章中，我们提供了作用于无限维复Banach空间的所有有界线性算子在代数上的所有映射的完整描述，这些映射在两个算子的乘积下使上升或下降保持不变。

引用次数: 0

Spectral extremal problem for the odd prism 奇棱镜的光谱极值问题

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2025-10-24 DOI: 10.1016/j.laa.2025.10.025

Xinhui Duan, Lu Lu

The spectral Turán number

spex (n, F)

denotes the maximum spectral radius

λ (G)

of an F-free graph G of order n. This paper determines

spex (n, C_{2 k + 1}^{□})

for sufficiently large n, establishing the unique extremal graph. Here,

C_{2 k + 1}^{□}

is the odd prism, which is the Cartesian product

C_{2 k + 1} □ K_{2}

, where the Cartesian product

G □ F

has vertex set

V (G) \times V (F)

, and edges between

(u_{1}, v_{1})

and

(u_{2}, v_{2})

if either

u_{1} = u_{2}

and

v_{1} v_{2} \in E (F)

, or

v_{1} = v_{2}

and

u_{1} u_{2} \in E (G)

谱Turán数spex（n，F）表示n阶无F图G的最大谱半径λ(G)。当n足够大时，确定了spex（n,C2k+1□），建立了唯一极值图。这里，C2k+1□是奇棱镜，它是笛卡尔积C2k+1□K2，其中笛卡尔积G□F具有顶点集V(G)×V(F)，并且在（u1,v1）和（u2,v2）之间有边，如果u1=u2和v1v2∈E(F)，或者v1=v2和u1u2∈E(G)。

引用次数: 0

Universal bound on the eigenvalues of 2-positive trace-preserving maps 2-正保持迹映射特征值的全称界

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2025-10-24 DOI: 10.1016/j.laa.2025.10.022

Frederik vom Ende , Dariusz Chruściński , Gen Kimura , Paolo Muratore-Ginanneschi

We prove an upper bound on the trace of any 2-positive, trace-preserving map in terms of its smallest eigenvalue. We show that this spectral bound is tight, and that 2-positivity is necessary for this inequality to hold in general. Moreover, we use this to infer a similar bound for generators of one-parameter semigroups of 2-positive trace-preserving maps. With this approach we generalize known results for completely positive trace-preserving dynamics while providing a significantly simpler proof that is entirely algebraic.

我们用最小特征值证明了任意2正、保迹映射的迹的上界。我们证明了这个谱界是紧的，并且2正性对于这个不等式一般成立是必要的。此外，我们还利用这一理论推导出了2正迹保持映射的单参数半群的生成器的类似界。用这种方法，我们推广了已知的完全正迹保持动力学的结果，同时提供了一个明显更简单的证明，这是完全代数的。

引用次数: 0

Keldysh's theorem revisited 再次回顾Keldysh定理

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2025-10-24 DOI: 10.1016/j.laa.2025.10.020

Johannes M. Schumacher

In a variety of applications, the problem comes up of describing the principal part of the inverse of a holomorphic operator at an eigenvalue in terms of left and right root functions associated to the eigenvalue. Such a description was given by Keldysh in 1951. His theorem, the proof of which was published only in 1971, is a fundamental result in the local spectral theory of operator-valued functions. Here we present a streamlined derivation in the matrix case, and we extend Keldysh's theorem by means of a new principal part formula. Special attention is given to the semisimple case (first-order poles).

在各种应用中，用与特征值相关的左右根函数来描述全纯算子在特征值处逆的主部的问题。这样的描述是Keldysh在1951年给出的。他的定理直到1971年才被证明，是算子值函数局部谱理论的一个基本结果。本文给出了矩阵情况下的简化推导，并利用一个新的主成分公式对Keldysh定理进行了推广。特别注意半简单情况（一阶极点）。

引用次数: 0

Spectral conditions for the maximum subgraph edge-connectivity of graphs 图的最大子图边连通性的谱条件

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2025-10-24 DOI: 10.1016/j.laa.2025.10.023

Jia Wei , Muhuo Liu , Zhifu You , Hong-Jian Lai

Let

κ^{'} (G)

be the edge connectivity of a graph G. The strength of G, denoted by

{\overline{κ}}^{'} (G)

, is the maximum value of

κ^{'} (H)

where H runs over all subgraphs of G. For a positive integer k, Mader in 1971 initiated the study of a simple graph G that does not have a subgraph with edge connectivity exceeding k but the addition of any edge to G will create a subgraph of edge connectivity at least

k + 1

. For any simple graph G on

n \geq k + 2

vertices with the spectral radius of

λ (G)

, we will show the followings:

(i) If the minimum degree of G is at least k, and

λ (G) \geq \frac{k - 1 + \sqrt{4 n k - 3 k^{2} - 2 k + 1}}{2},

then

{\overline{κ}}^{'} (G) > k

unless G belongs to a well classified family of graphs.

(ii) If

k \geq 2

and

λ (G) \leq k + 1

, then there exists an edge

e \in E (G^{c})

such that

{\overline{κ}}^{'} (G + e) \leq k

unless G belongs to a well classified family of graphs.

设κ ' (G)是图G的边连通性。G的强度，用κ ' (G)表示，是κ ' (H)的最大值，其中H运行在G的所有子图上。对于一个正整数k， Mader在1971年开始研究一个简单图G，它没有一个边连通性超过k的子图，但是向G添加任何一条边将创建一个边连通性至少为k+1的子图。对于任意简单图G，在n≥k+2个顶点上，谱半径为λ(G)，我们将证明如下：(i)如果G的最小度至少为k，并且λ(G)≥k−1+4nk−3k2−2k+12，则κ的' (G)>k，除非G属于一个分类良好的图族。（ii）如果k≥2且λ(G)≤k+1，则存在一条边e∈e （Gc）使得κ的(G+e)≤k，除非G属于一个分类良好的图族。

引用次数: 0

Two-sided preconditioned CGLS for the solution of factorized linear systems 分解线性系统解的双面预条件CGLS

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2025-10-24 DOI: 10.1016/j.laa.2025.10.018

Yurui Jiang , Junfeng Yin

Two-sided preconditioned CGLS method is proposed for solving large-scale rank-deficient factorized linear systems, where the original system is reformulated into an augmented linear system with a scaling parameter. A class of structured two-sided preconditioners based on sketching-and-QR strategy is studied in detail. The convergence theory of the proposed method is established and the properties of the preconditioned system are analyzed. Numerical experiments demonstrate that the proposed method with sketch-based preconditioners is efficient and outperforms existing approaches.

提出了求解大规模秩缺位分解线性系统的双侧预条件CGLS方法，该方法将原系统重构为带尺度参数的增广线性系统。详细研究了一类基于草图- qr策略的结构化双面预调节器。建立了该方法的收敛性理论，分析了预条件系统的性质。数值实验表明，采用基于草图的预调节器的方法是有效的，并且优于现有的方法。

引用次数: 0

The ±-rank of a (0,±1)-matrix （0，±1）矩阵的±秩

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2025-10-24 DOI: 10.1016/j.laa.2025.10.021

Richard A. Brualdi , Geir Dahl

We introduce and study a new rank of

(0, \pm 1)

-matrices generalizing both the binary rank and the term rank of

(0, 1)

-matrices. We call it the ±-rank of a

(0, \pm 1)

-matrix. We establish several inequalities relating the different ranks, including ordinary real rank. Moreover, the ±-rank is discussed for certain classes of

(0, \pm 1)

-matrices, such as alternating sign matrices (ASMs), network matrices, and matrices whose bipartite graph is a tree. Computationally the ±-rank is not easy to determine (like binary rank it may be an NP-hard problem), and we investigate several examples.

我们引入并研究了一种新的（0，±1）矩阵秩，它推广了（0,1）矩阵的二秩和项秩。我们称它为（0，±1）矩阵的±秩。我们建立了几个关于不同等级的不等式，包括普通实际等级。此外，还讨论了某些（0，±1）-矩阵的±-秩，如交替符号矩阵、网络矩阵和二部图为树的矩阵。计算±-秩不容易确定（像二进制秩一样，它可能是一个np困难问题），我们研究了几个例子。

引用次数: 0

Maximum spectral gaps of graphs 图的最大谱隙

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2025-10-24 DOI: 10.1016/j.laa.2025.10.024

George Brooks , William Linz , Linyuan Lu

The spread of a graph G is the difference

λ_{1} - λ_{n}

between the largest and smallest eigenvalues of its adjacency matrix. Breen, Riasanovsky, Tait and Urschel recently determined the graph on n vertices with maximum spread for sufficiently large n. In this paper, we study a related question of maximizing the difference

λ_{i + 1} - λ_{n - j}

for a given pair

(i, j)

over all graphs on n vertices. We give upper bounds for all pairs

(i, j)

, exhibit an infinite family of pairs where the bound is tight, and show that for the pair

(1, 0)

the extremal example is unique. These results contribute to a line of inquiry pioneered by Nikiforov aiming to maximize different linear combinations of eigenvalues over all graphs on n vertices.

图G的扩展是其邻接矩阵的最大特征值和最小特征值之间的差λ1−λn。Breen, Riasanovsky， Tait和Urschel最近确定了n个顶点上的图在足够大的n下具有最大的扩展。在本文中，我们研究了给定对（i,j）在所有n个顶点上的差值λi+1−λn−j最大化的相关问题。我们给出了所有对（i,j）的上界，展示了一个无限族的紧界对，并证明了对（1,0）的极值例子是唯一的。这些结果有助于Nikiforov开创的一系列研究，旨在最大化n个顶点上所有图的特征值的不同线性组合。

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引用次数: 0

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