Linear Algebra and its Applications最新文献

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A spectral analogue of Ore's problem on Turán theorem 关于Turán定理的Ore问题的谱模拟

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-04-15 Epub Date: 2026-01-13 DOI: 10.1016/j.laa.2026.01.012

Lele Liu , Bo Ning

We establish a spectral counterpart to Ore's problem (1962) which asks for the maximum size of an n-vertex graph such that its complement is connected and does not contain

K_{r + 1}

as a subgraph, where

K_{r + 1}

is a clique of order

r + 1

. Specifically, we characterize the unique graph achieving the maximum spectral radius among all n-vertex,

K_{r + 1}

-free graphs with connected complements. The proof strategy combines the association of the extremal graph with an auxiliary tree to infer its structure and technical spectral analysis of the extremal graphs' Perron vector.

我们建立了一个谱对应于Ore的问题（1962），该问题要求n顶点图的最大尺寸，使得它的补是连通的，并且不包含Kr+1作为子图，其中Kr+1是r+1阶的团。具体地说，我们描述了在所有n顶点，具有连通补的Kr+1自由图中实现最大谱半径的唯一图。该证明策略结合了极值图与辅助树的关联来推断其结构和极值图的Perron向量的技术谱分析。

引用次数: 0

Commuting graphs of p-adic matrices p进矩阵的交换图

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-04-15 Epub Date: 2026-01-15 DOI: 10.1016/j.laa.2026.01.008

Ralph Morrison

We study the commuting graph of

n \times n

matrices over the field of p-adics

Q_{p}

, whose vertices are non-scalar

n \times n

matrices with entries in

Q_{p}

and whose edges connect pairs of matrices that commute under matrix multiplication. We prove that this graph is connected if and only if

n \geq 3

, with n neither prime nor a power of p. We also prove that in the case of

p = 2

and

n = 2 q

for q a prime with

q \geq 7

, the commuting graph has the maximum possible diameter of 6; these are the first known such examples independent of the axiom of choice. We also find choices of p and n yielding diameter 4 and diameter 5 commuting graphs, and prove general bounds depending on p and n.

研究了p-adics Qp域上n×n矩阵的交换图，其顶点为具有Qp中条目的非标量n×n矩阵，其边连接在矩阵乘法下交换的矩阵对。证明了当且仅当n≥3，且n既不是素数，也不是p的幂时，交换图是连通的。还证明了在p=2, n=2q的情况下，对于q≥7的素数，交换图的最大可能直径为6；这是已知的第一个独立于选择公理的例子。我们还找到了产生直径4和直径5交换图的p和n的选择，并证明了依赖于p和n的一般界。

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引用次数: 0

Log-majorizations between quasi-geometric type means for matrices 矩阵的拟几何型均值之间的对数最大化

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-04-15 Epub Date: 2026-01-12 DOI: 10.1016/j.laa.2026.01.003

Fumio Hiai

In this paper, for

α \in (0, \infty) ∖ {1}

p > 0

and positive semidefinite matrices A and B, we consider the quasi-extensions

M_{α, p} (A, B) : = M_{α} {(A^{p}, B^{p})}^{1 / p}

of several α-weighted geometric type matrix means

M_{α} (A, B)

such as the α-weighted geometric mean in Kubo–Ando's sense, the Rényi mean, etc. The log-majorization

M_{α, p} (A, B) ≺_{\log} N_{α, q} (A, B)

is examined for pairs

(M, N)

of those α-weighted geometric type means. The joint concavity/convexity of the trace functions

Tr M_{α, p}

is also discussed based on theory of quantum divergences.

本文对α∈(0,∞)∈{1},p>；0和正半定矩阵A和B，考虑了几个α-加权几何型矩阵均值m - α，p(A，B):= m - α(Ap,Bp)1/p的拟扩展，如Kubo-Ando意义上的α-加权几何均值，rsamnyi均值等。对这些α-加权几何型均值的对（M，N），检验了Mα，p(A，B),q（A，B）的对数化。基于量子散度理论讨论了迹函数TrMα，p的联合凹凸性。

引用次数: 0

Derived equivalences between defective rectangles 导出了缺陷矩形之间的等价

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-04-15 Epub Date: 2026-01-20 DOI: 10.1016/j.laa.2026.01.019

Qiang Dong , Shunye Li

In this article, we present quiver realizations of two classes of algebras that are derived equivalent to upper triangular matrix algebras. We investigate defective rectangle algebras and show that four of them are derived equivalent. Moreover, we establish derived equivalences between certain defective rectangle algebras and Nakayama algebras.

在本文中，我们给出了等价于上三角矩阵代数的两类代数的颤振实现。研究了有缺陷的矩形代数，并证明了其中的四个代数是等价的。此外，我们还建立了某些缺陷矩形代数与中山代数之间的推导等价。

引用次数: 0

Numerical radius and ℓp operator norm of Kronecker products and Schur powers: inequalities and equalities Kronecker积和Schur幂的数值半径和p算子范数：不等式和等式

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-04-15 Epub Date: 2026-01-09 DOI: 10.1016/j.laa.2026.01.005

Pintu Bhunia , Sujit Sakharam Damase , Apoorva Khare

<div><div>Suppose <math><mi>A</mi><mo>=</mo><mo>[</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>]</mo><mo>∈</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>C</mi><mo>)</mo></math> is a complex <math><mi>n</mi><mo>×</mo><mi>n</mi></math> matrix and <math><mi>B</mi><mo>∈</mo><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math> is a bounded linear operator on a complex Hilbert space <math><mi>H</mi></math>. We show that <math><mi>w</mi><mo>(</mo><mi>A</mi><mo>⊗</mo><mi>B</mi><mo>)</mo><mo>≤</mo><mi>w</mi><mo>(</mo><mi>C</mi><mo>)</mo></math>, where <math><mi>w</mi><mo>(</mo><mo>⋅</mo><mo>)</mo></math> denotes the numerical radius and <math><mi>C</mi><mo>=</mo><mo>[</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>]</mo></math> with <math><msub><mrow><mi>c</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><mi>w</mi><mrow><mo>(</mo><mrow><mo>[</mo><mtable><mtr><mtd><mn>0</mn></mtd><mtd><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></mtd></mtr><mtr><mtd><msub><mrow><mi>a</mi></mrow><mrow><mi>j</mi><mi>i</mi></mrow></msub></mtd><mtd><mn>0</mn></mtd></mtr></mtable><mo>]</mo></mrow><mo>⊗</mo><mi>B</mi><mo>)</mo></mrow></math>. This refines Holbrook's classical bound <math><mi>w</mi><mo>(</mo><mi>A</mi><mo>⊗</mo><mi>B</mi><mo>)</mo><mo>≤</mo><mi>w</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>‖</mo><mi>B</mi><mo>‖</mo></math> (1969) [31], when all entries of A are non-negative. If moreover <math><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi><mi>i</mi></mrow></msub><mo>≠</mo><mn>0</mn></math> ∀i, we prove that <math><mi>w</mi><mo>(</mo><mi>A</mi><mo>⊗</mo><mi>B</mi><mo>)</mo><mo>=</mo><mi>w</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>‖</mo><mi>B</mi><mo>‖</mo></math> if and only if <math><mi>w</mi><mo>(</mo><mi>B</mi><mo>)</mo><mo>=</mo><mo>‖</mo><mi>B</mi><mo>‖</mo></math>. We then extend these and other results to the more general setting of semi-Hilbertian spaces induced by a positive operator.</div><div>In the reverse direction, we also specialize these results to Kronecker products and hence to Schur/entrywise products, of matrices: (1)(a) We first provide an alternate proof (using <math><mi>w</mi><mo>(</mo><mi>A</mi><mo>)</mo></math>) of a result of Goldberg and Zwas (1974) [24] that if the spectral norm of A equals its spectral radius, then each Jordan block for each maximum-modulus eigenvalue must be <math><mn>1</mn><mo>×</mo><mn>1</mn></math> (“partial diagonalizability”). (b) Using our approach, we further show given <math><mi>m</mi><mo>≥</mo><mn>1</mn></math> that <math><mi>w</mi><mo>(</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>∘</mo><mi>m</mi></mrow></msup><mo>)</mo><mo>

假设A=[aij]∈Mn(C)是一个复n×n矩阵，B∈B(H)是复Hilbert空间H上的一个有界线性算子，我们证明了w(A⊗B)≤w(C)，其中w（⋅）表示数值半径，C=[cij], cij=w（[0aijaji0]⊗B）。这改进了Holbrook的经典界w(A⊗B)≤w(A)‖B‖（1969）[31]，当A的所有项都是非负的。如果aii≠0∀i，我们证明w(A⊗B)=w(A)‖B‖当且仅当w(B)=‖B‖。然后，我们将这些结果和其他结果推广到由正算子导出的半希尔伯特空间的更一般的设置。在相反的方向上，我们也将这些结果专门用于矩阵的Kronecker积和Schur/entrywise积：(1)(a)我们首先提供Goldberg和Zwas(1974)[24]的结果的替代证明（使用w(a)），如果a的谱范数等于它的谱半径，那么每个最大模特征值的每个Jordan块必须是1×1（“部分对角化”）。(b)使用我们的方法，我们进一步证明当m≥1时w(A°m)≤wm(A)——我们也在这里描述了当等式成立时的特征。(2)我们给出了所有A∈Mn(C)的p算子范数和A⊗B的数值半径的上界和下界，当约束于双随机矩阵A时，它们是相等的。最后，利用这些上界，我们得到了对任意复数多项式根的改进估计。

引用次数: 0

Spectral radius and rainbow k-factors of graphs 图的光谱半径和彩虹k因子

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-04-15 Epub Date: 2026-01-23 DOI: 10.1016/j.laa.2026.01.022

Liwen Zhang, Zhiyuan Zhang

Let

G = {G_{1}, \dots, G_{\frac{k n}{2}}}

be a set of graphs on the same vertex set

V = {1, \dots, n}

where

k \cdot n

is even. We say

G

admits a rainbow k-factor if there exists a k-regular graph F on the vertex set V such that all edges of F are from different members of

G

. In this paper, we show a sufficient spectral condition for the existence of a rainbow k-factor for

k \geq 2

, which is that if

ρ (G_{i}) \geq ρ (K_{k - 1} \lor (K_{1} \cup K_{n - k}))

for each

G_{i} \in G

, then

G

admits a rainbow k-factor unless

G_{1} = G_{2} = \dots = G_{\frac{k n}{2}} ≅ K_{k - 1} \lor (K_{1} \cup K_{n - k})

设G={G1，…，Gkn2}是同一顶点集V={1，…，n}上的图的集合，其中k·n为偶。如果在顶点集V上存在一个k正则图F，使得F的所有边都来自G的不同元素，我们说G存在彩虹k因子。在本文中，我们给出了k≥2时彩虹k因子存在的一个谱充分条件，即对于每个Gi∈G，如果ρ(Gi)≥ρ(Kk−1∨(K1∪Kn−k))，则G存在彩虹k因子，除非G1=G2=⋯=Gkn2≠Kk−1∨(K1∪Kn−k)。

引用次数: 0

On representations of GL2 over finite chain rings 有限链环上GL2的表示

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-04-01 Epub Date: 2026-01-02 DOI: 10.1016/j.laa.2025.12.023

Prem Dagar, Mahendra Kumar Verma

Let F be a non-Archimedean local field and

O

be its ring of integers with ϖ chosen as a fixed generator for the maximal ideal of

O

. Define

O_{ℓ} : = O / 〈 ϖ^{ℓ} 〉

as the finite local ring. In this paper, we describe the explicit construction of parabolically induced representations of the group

{GL}_{2} (O_{ℓ})

for

ℓ > 1

and establish an irreducibility criterion for these representations. Additionally, we determine the number of irreducible constituents in the case of reducibility. Furthermore, we study the primitive cuspidal representations and explore the representations of

{GL}_{2} (O_{ℓ})

using the Whittaker and Kirillov model.

设F是一个非阿基米德局部域，O是它的整数环，其中选择π作为O的最大理想的固定发生器。定义O n:=O/ < O n >作为有限局部环。本文给出了群GL2(O)对l >；1的抛物诱导表示的显式构造，并建立了这些表示的不可约准则。此外，我们确定在可还原性的情况下不可还原性成分的数量。此外，我们研究了原始的反转表示，并利用Whittaker和Kirillov模型探索了GL2(O)的表示。

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引用次数: 0

Tangent Lie algebras of automorphism groups of free algebras 自由代数的自同构群的切李代数

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-04-01 Epub Date: 2026-01-07 DOI: 10.1016/j.laa.2025.12.020

Ivan Shestakov , Ualbai Umirbaev

We study an analogue of the Andreadakis–Johnson filtration for automorphism groups of free algebras and introduce the notion of tangent Lie algebras for certain automorphism groups, defined as subalgebras of the Lie algebra of derivations. We show that, for many classical varieties of algebras, the tangent Lie algebra is contained in the Lie algebra of derivations with constant divergence. We also introduce the concepts of approximately tame and absolutely wild automorphisms of free algebras in arbitrary varieties and employ tangent Lie algebras to investigate their properties. It is shown that nearly all known examples of wild automorphisms of free algebras are absolutely wild, with the notable exceptions of the Nagata and Anick automorphisms. We show that the Bergman automorphism of free matrix algebras of order two is absolutely wild. Furthermore, we prove that free algebras in any variety of polynilpotent Lie algebras–except for the abelian and metabelian varieties–also possess absolutely wild automorphisms.

我们研究了自由代数自同构群的andreadakisjohnson滤除的一个类似，并引入了某些自同构群的切李代数的概念，定义为派生李代数的子代数。我们证明了对于许多经典代数变体，切李代数包含在具有常散度导数的李代数中。我们还引入了任意变异的自由代数的近似驯服自同构和绝对野生自同构的概念，并利用切李代数研究了它们的性质。证明了除了Nagata自同构和Anick自同构外，几乎所有已知的自由代数的野生自同构都是绝对野生的。我们证明了二阶自由矩阵代数的Bergman自同构是绝对狂野的。此外，我们证明了除阿贝尔和亚贝尔变体外，任意多幂零李代数变种中的自由代数也具有绝对野生自同构。

引用次数: 0

Multiplicative trace and spectrum preservers on stochastic matrices 随机矩阵上的乘迹和谱保持器

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-04-01 Epub Date: 2026-01-05 DOI: 10.1016/j.laa.2025.12.019

Ming-Cheng Tsai , Huajun Huang

We characterize maps

ϕ_{i} : S \to S

i = 1, \dots, m

and

m \geq 1

, that have the multiplicative spectrum or trace preserving property:

spec (ϕ_{1} (A_{1}) \dots ϕ_{m} (A_{m})) = spec (A_{1} \dots A_{m}), or tr (ϕ_{1} (A_{1}) \dots ϕ_{m} (A_{m})) = tr (A_{1} \dots A_{m}),

where

S

is the set of

n \times n

doubly stochastic, row stochastic, or column stochastic matrices, or the space spanned by one of these sets. Linearity is assumed when

m = 1

. We show that every stochastic matrix contains a real doubly stochastic component that carries the spectral information. In consequence, the multiplicative spectrum or trace preservers on these sets

S

are linked to the corresponding preservers on the space of doubly stochastic matrices. Moreover, when

m \geq 3

, multiplicative trace preservers always coincide with multiplicative spectrum preservers.

我们描述具有乘法谱或迹保持性质的映射，即：spec(ϕ1(A1)⋯ϕm(Am))=spec(A1⋯Am),ortr(ϕ1(A1)⋯ϕm(Am))=tr(A1⋯Am)，其中S是n×n双随机、行随机或列随机矩阵的集合，或由这些集合之一所跨越的空间。当m=1时，假设线性。我们证明了每个随机矩阵包含一个实双随机分量，它携带谱信息。因此，这些集合S上的乘谱守恒或迹守恒与双随机矩阵空间上相应的守恒相联系。此外，当m≥3时，乘性迹保持器总是与乘性谱保持器重合。

引用次数: 0

Testing isomorphism between tuples of subspaces 测试子空间元组之间的同构性

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-04-01 Epub Date: 2026-01-02 DOI: 10.1016/j.laa.2025.12.021

Emily J. King , Dustin G. Mixon , Shayne Waldron

Given two tuples of subspaces, can you tell whether the tuples are isomorphic? We develop theory and algorithms to address this fundamental question. We focus on isomorphisms in which the ambient vector space is acted on by either a unitary group or general linear group. If isomorphism also allows permutations of the subspaces, then the problem is at least as hard as graph isomorphism. Otherwise, we provide a variety of polynomial-time algorithms with Matlab implementations to test for isomorphism.

给定两个子空间的元组，你能判断这两个元组是否同构吗？我们发展理论和算法来解决这个基本问题。我们关注环境向量空间被酉群或一般线性群作用的同构。如果同构也允许子空间的置换，那么这个问题至少和图同构一样难。另外，我们提供了各种多项式时间算法与Matlab实现来测试同构。

引用次数: 0

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Linear Algebra and its Applications

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