Kijti Rodtes, Mutti Ur Rehman Abbasi
In this paper, the exact values of the structured singular values of some generalized stochastic complex matrices is explicit in term of the constant row (column) sum.
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Structured pseudospectrum and structured condition pseudospectrum of non-archimedean matrices
本文定义非阿基米德矩阵及其矩阵束的结构伪谱，证明相关性质并给出示例。
The subject of Chapter 1 is GKK $τ$-matrices and related topics. Chapter 2 is devoted to boundedly invertible collections of matrices, with applications to operator norms and spline approximation. Various structured matrices (Toeplitz, Hessenberg, Hankel, Cauchy, and other) are used extensively throughout the thesis.
Structured Linearizations of Structured Rational Matrices
本文提出了一种结构化线性化方法，用于保持有理矩阵的结构特性，以提高计算稳定性与准确性。
On the inversion of the block double-structured and of the triple-structured Toeplitz matrices and on the corresponding reflection coefficients
本文在已有二维TBT矩阵求逆刻画基础上，将方法推广到分块TBT矩阵与三维Toeplitz矩阵，研究其逆矩阵恢复所需最小信息及相应反射系数。
For an (indefinite) scalar product $[x,y]_B = x^HBy$ for $B= \pm B^H \in Gl_n(\mathbb{C})$ on $\mathbb{C}^n \times \mathbb{C}^n$ we show that the set of diagonalizable matrices is dense in the set of all $B$-selfadjoint, $B$-skewadjoint, $B$-unitary and $B$-normal matrices.
We present two generalisations of Singular Value Decomposition from real-numbered matrices to dual-numbered matrices. We prove that every dual-numbered matrix has both types of SVD. Both of our generalisations are motivated by applications, either to geometry or to mechanics.
This note describes a technique for generating large non-singular matrices with blocks of full rank. Our motivation to construct such matrices arises in the white-box implementation of cryptographic algorithms with S-boxes.
I provide an alternate and self-contained proof of Botha's theorem on products of idempotent and square-zero matrices where the product contains two square-zero factors, and provide a conclusive characterisation of products of singular quadratic matrices based on previous results.
In this paper we provide concrete constructions of idempotents to represent typical singular matrices over a given ring as a product of idempotents and apply these factorizations for proving our main results. We generalize works due to Laffey (Products of idempotent matrices. Linear Multilinear A. 1983) and Rao (Products of idempotent matrices. Linear Algebra Appl. 2009) to noncommutative setting and fill in the gaps in the original proof of Rao's main theorems. We also consider singular matrices over Bézout domains as to when such a matrix is a product of idempotent matrices.
The Strong Singular Value Property for Matrices
本文引入并发展了矩阵的强奇异值性质，用以研究哪些非负实数列表可作为具有指定零-非零模式的矩阵的奇异值。
Given an arbitrary field K, we reduce the determination of the singular endomorphisms $f$ of M_n(K) that stabilize GL_n(K) to the classification of n-dimensional division algebras over K. Our method, which is based upon Dieudonné's theorem on singular subspaces of M_n(K), also yields a proof for the classical non-singular case.
We introduce right eigenvalues and subeigenvalues for square dual complex matrices. An $n \times n$ dual complex Hermitian matrix has exactly $n$ right eigenvalues and subeigenvalues, which are all real. The Hermitian matrix is positive semi-definite or definite if and only if all of its right eigenvalues and subeigenvalues are nonnegative or positive, respectively. A Hermitian matrix can be diagonalized if and only if it has no right subeigenvalues. Then we present the singular value decomposition for general dual complex matrices. The results are further extended to dual quaternion matrices.
We give a detailed account of various connections between several classes of objects: Hankel, Hurwitz, Toeplitz, Vandermonde and other structured matrices, Stietjes and Jacobi-type continued fractions, Cauchy indices, moment problems, total positivity, and root localization of univariate polynomials. Along with a survey of many classical facts, we provide a number of new results.
Let $k = \mathbb{Q}(\sqrtα)$ be a real quadratic number field, where $α$ is a positive square-free integer. Let $\mathcal{O}_k$ be the ring of integers of $k$. In this paper, we prove that a certain set of $2 \times 2$ singular matrices with entries in $\mathcal{O}_k$ can be written as a product of a bounded number of idempotent matrices. Our main theorem can be viewed as a generalization of the recent result by Cossu and Zanardo, which studies finite generation of certain singular matrices by idempotent matrices over $\mathcal{O}_k$ instead of bounded generation of certain singular matrices b…
Core EP, Dual Core EP and Composite Generalized Inverses for a Class of Structured Matrices
研究双星有向图关联矩阵的广义反演，推导核心、双核、核心EP和双核EP的显式块公式及存在条件，结合Moore-Penrose和核心型反演得到其他复合伪反演。
Invertibility of structured perturbations of singular matrices over unital rings
本文研究单位环上奇异矩阵经结构化扰动后的可逆性，证明在核与像的自然假设下可逆性等价于扰动矩阵可逆，并给出逆的显式公式，推广了Eriksson和Nordqvist的定理。
Constructing Superregular Matrices
本文研究了超正则矩阵的构造问题，提出了一种基于 Kronecker 积的块超正则矩阵构造方法，以及两种通过较小域上较小超正则矩阵构造超正则矩阵的方法。
Groups of singular alternating sign matrices
本文研究由奇异交错符号矩阵构成的乘法群，给出构造方法，证明任意有限群均可如此表示，并探讨矩阵大小、秩与乘法阶的关系。
It is well known that any nonsingular M-matrix admits an LU factorization into M-matrices (with L and U lower and upper triangular respectively) and any singular M-matrix is permutation similar to an M-matrix which admits an LU factorization into M-matrices. Varga and Cai establish necessary and sufficient conditions for a singular M-matrix (without permutation) to allow an LU factorization with L nonsingular. We generalize these results in two directions. First, we find necessary and sufficient conditions for the existence of an LU factorization of a singular M-matrix where L and U are both p…
Making matrices better: Geometry and topology of polar and singular value decomposition
从几何与拓扑角度研究固定尺寸矩阵空间，探讨不同秩家族及其关联，分析矩阵的最近正交邻近和最近奇异邻近，以及极值和奇异值分解及其应用。
Necessary and Sufficient Criterion for Singular or Nonsingular of Diagonally Dominant Matrices
本文提出对对角占优矩阵奇异性的必要和充分条件，通过角度方程组和相似性分析，结合网络动力系统等应用，解决矩阵奇异性的判定问题。
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