Linear Algebra and its Applications最新文献

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Some simplified formulas for the matched projection of an idempotent 幂等函数的匹配投影的一些简化公式

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-01-13 DOI: 10.1016/j.laa.2026.01.010

Qingxiang Xu

Let

L (H)

be the set of all adjointable operators on a Hilbert

C^{⁎}

-module H. For each

T \in L (H)

T^{⁎}

denotes its adjoint operator, and

| T |

is the positive square root of

T^{⁎} T

. We establish simplified formulas for the matched projection

m (Q)

of an idempotent

Q \in L (H)

m (Q) = \frac{I + | Q^{⁎} | - | I - Q^{⁎} |}{2} = \frac{I + | Q | - | I - Q |}{2} = \frac{2 + | Q + Q^{⁎} | - | 2 - (Q + Q^{⁎}) |}{4},

where I is the identity operator on H. These explicit expressions facilitate the straightforward derivation of several known properties of

m (Q)

设L(H)是Hilbert C _ -模H上所有可伴随算子的集合。对于每一个T∈L(H)， T _表示它的伴随算子，|T|是T _ T的正平方根。我们建立了幂等Q∈L(H) asm(Q)=I+|Q |−|I−Q|2= I+|Q|−|I−Q|2=2+|Q+Q |−|2−(Q+Q)|4的匹配投影m(Q)的简化公式，其中I是H上的恒等算子。这些显式表达式有助于直接推导出m(Q)的几个已知性质。

引用次数: 0

Bounds on hypergraph energy and its variation under arbitrary hyperedge deletion 任意超边删除下的超图能量界及其变化

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-01-13 DOI: 10.1016/j.laa.2026.01.004

Shib Sankar Saha , Swarup Kumar Panda

The energy of a hypergraph

H

is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix

A (H)

. In 2022, K. Cardoso et al. showed through examples that removing an arbitrary hyperedge from a hypergraph may increase, decrease, or leave its energy unchanged. In this article, we prove that for a k-uniform complete hypergraph and a 3-uniform complete bipartite hypergraph, the energy always decreases when an arbitrary hyperedge is deleted. Furthermore, we establish both lower and upper bounds for the energy of k-uniform hypergraphs in terms of the minimum degree and the strong chromatic number.

超图H的能量定义为它的邻接矩阵a (H)的特征值的绝对值之和。2022年，K. Cardoso等人通过实例表明，从超图中移除任意一个超边缘可能会增加、减少或保持其能量不变。在本文中，我们证明了对于k-一致完全超图和3-一致完全二部超图，当任意超边被删除时，能量总是减小的。进一步，我们用最小度和强色数建立了k-一致超图的能量下界和上界。

引用次数: 0

Alternating and symmetric superpowers of metric generalized Jordan superpairs 度量广义Jordan超对的交替和对称超幂

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-01-13 DOI: 10.1016/j.laa.2026.01.007

Diego Aranda-Orna , Alejandra S. Córdova-Martínez

The aim of this paper is to define and study the constructions of alternating and symmetric (super)powers of metric generalized Jordan (super)pairs. These constructions are obtained by transference via the Faulkner construction. The construction of tensor (super)products for metric generalized Jordan (super)pairs is revisited. We always assume that the characteristic of the base field

F

is different from 2; in case of positive characteristic, sometimes we require that the characteristic is large enough to allow nondegeneracy of certain bilinear forms.

本文的目的是定义和研究度量广义Jordan（超）对的交替对称（超）幂的构造。这些结构是通过福克纳结构的移情而获得的。重新研究了度量广义约当（超）对的张量（超）积的构造。我们总是假设基场的特性F不同于2；在正特征的情况下，有时我们要求特征足够大以允许某些双线性形式的不退化。

引用次数: 0

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 : 2026-01-13 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

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 : 2026-01-12 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

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 : 2026-01-09 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

Maps on B(X) preserving k-potent operators B(X)上保留k-有效算子的映射

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-01-09 DOI: 10.1016/j.laa.2026.01.006

Hassane Benbouziane, Kaddour Chadli, Mustapha Ech-chérif El Kettani

Let

B (X)

be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space

X

. For a fixed integer

k \geq 2

, an operator

A \in B (X)

is called k-potent operator if

A^{k} = A

. In this paper, we provide a complete description of all surjective and weakly continuous maps

Φ : B (X) \to B (X)

such that

A - λ B

is k-potent operator if and only if

Φ (A) - λ Φ (B)

is k-potent operator, for any

A, B \in B (X)

and

λ \in C

. We also give the result in the setting of complex Hilbert spaces without the hypothesis of continuity.

设B(X)为无穷维复Banach空间X上所有有界线性算子的代数。对于固定整数k≥2，当Ak= a时，算子a∈B(X)称为k强算子。本文给出了所有满射弱连续映射Φ：B(X)→B(X)的完备描述，当且仅当Φ(a)−λΦ(B)是k强算子时，对于任意a，B∈B(X), λ∈C， a−λB是k强算子。我们也给出了在没有连续性假设的复希尔伯特空间下的结果。

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 : 2026-01-07 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

From the Editor-in-Chief 来自总编辑

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-01-06 DOI: 10.1016/j.laa.2026.01.001

Richard A. Brualdi

引用次数: 0

Systems of standard and conjugate Sylvester equations: a characterization for the uniqueness of solution 标准和共轭Sylvester方程组：解的唯一性的表征

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications

Pub Date : 2026-01-06 DOI: 10.1016/j.laa.2026.01.002

Fernando De Terán , Bruno Iannazzo

We provide a characterization for a periodic system of generalized Sylvester and conjugate-Sylvester equations, with at most one generalized conjugate-Sylvester equation, to have a unique solution when all coefficient matrices are square and all unknown matrices of the system have the same size. We also present a procedure to reduce an arbitrary system of generalized Sylvester and conjugate-Sylvester equations to periodic systems having at most one generalized conjugate-Sylvester equation. Therefore, the obtained characterization for the uniqueness of solution of periodic systems provides a characterization for general systems of generalized Sylvester and conjugate-Sylvester equations.

给出了一个由广义Sylvester方程和共轭Sylvester方程组成的周期系统，当系统中所有的系数矩阵都是平方矩阵，且系统中所有的未知矩阵大小相同时，系统有唯一解的性质，且系统中最多有一个广义共轭Sylvester方程。我们也给出了将任意的广义Sylvester方程和共轭Sylvester方程组成的系统化为至多有一个广义共轭Sylvester方程的周期系统的过程。因此，所得到的周期系统解的唯一性刻划为广义Sylvester方程和共轭Sylvester方程的一般系统提供了一个刻划。

引用次数: 0

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