Anders Skovsted Buch
We give a minimal list of inequalities characterizing the possible eigenvalues of a set of Hermitian matrices with positive semidefinite sum of bounded rank. This answers a question of A. Barvinok.
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We study analogues of classical inequalities for the eigenvalues of sums of pseudo-Hermitian matrices.
Any set of $σ$-Hermitian matrices of size $n \times n$ over a field with involution $σ$ gives rise to a projective line in the sense of ring geometry and a projective space in the sense of matrix geometry. It is shown that the two concepts are based upon the same set of points, up to some notational differences.
We discuss our preliminary attempts to extend previous work on 2x2 Hermitian octonionic matrices with non-real eigenvalues to the 3x3 case.
Diagonalization of skew-Hermitian dual quaternion matrices and $ϕ$-Hermitian dual quaternion matrices
本文研究斜厄米对偶四元数矩阵的酉等价对角化，以及单位四元数$\phi$对应的$\phi$-厄米对偶四元数矩阵的酉$\phi$-相合对角化，推广了相关矩阵分解结论。
We show that any 3-component octonionic vector which is purely imaginary, but not quaternionic, is an eigenvector of a 6-parameter family of Hermitian octonionic matrices, with imaginary eigenvalue equal to the associator of its elements.
We extend previous work on the eigenvalue problem for Hermitian octonionic matrices by discussing the case where the eigenvalues are not real, giving a complete treatment of the 2x2 case, and summarizing some prelimenary results for the 3x3 case.
Moore Determinant of Dual Quaternion Hermitian Matrices
该研究将四元数埃尔米特矩阵的Chen、Moore行列式推广到对偶四元数埃尔米特矩阵，证明两类行列式相等且等于特征值乘积，还研究了其特征多项式。
We equip the complex polynomial algebra C[t] with the involution which is the identity on C and sends t to -t. Answering a question raised by V.G. Kac, we show that every hermitian or skew-hermitian matrix over this algebra is congruent to the direct sum of 1 by 1 matrices and 2 by 2 matrices with zero diagonal. Morevover, we show that if two n by n hermitian or skew-hermitian matrices have the same invariant factors, then they are congruent. The complex field can be replaced by any algebraically closed field of characteristic not 2.
Answering a question raised by S. Friedland, we show that the possible eigenvalues of Hermitian matrices (or compact operators) A, B, and C with C <= A + B are given by the same inequalities as in Klyachko's theorem for the case where C = A + B, except that the equality corresponding to tr(C) = tr(A) + tr(B) is replaced by the inequality corresponding to tr(C) <= tr(A) + tr(B). The possible types of finitely generated torsion modules A, B, and C over a discrete valuation ring such that there is an exact sequence B -> C -> A are characterized by the same inequalities.
Eigenvalues of Dual Hermitian Matrices with Application in Formation Control
本文提出补充矩阵方法计算对偶Hermitian矩阵特征值，并将其与单位增益图理论结合，为多智能体编队控制中的相对构型可行性问题提供跨学科求解途径。
We use symbolic expressions for traces of positive integer powers of a Hermitian operator (or, equivalently, coefficients of corresponding characteristic polynomial) to find solutions for the problems as follows: Factorization of characteristic polynomial that collects all eigenvalues that have the same multiplicity into one polynomial factor with coefficients rationally expressed through coefficients of original characteristic polynomial. Finding with any accuracy a minimal distance between eigenvalues, as well as a minimal and a maximal eigenvalues of the Hermitian operator, applying only ra…
Hua's fundamental theorem of geometry of hermitian matrices characterizes all bijective maps on the space of all hermitian matrices, which preserve adjacency in both directions. In this and subsequent paper we characterize maps on the set of all invertible hermitian matrices over a finite field, which preserve adjacency in one direction. This and author's previous result are used to obtain two new results related to maps that preserve the `speed of light' on finite Minkowski space-time. In this first paper it is shown that maps that preserve adjacency on the set of all invertible hermitian mat…
Denton, Parke, Tao and Zhang gave a new method which determines eigenvectors from eigenvalues for Hermitian matrices with distinct eigenvalues. In this short note, we extend the above result to general Hermitian matrices.
Jordan triple product homomorphisms on Hermitian matrices of dimension two
本文完整刻画了二维Hermitian复矩阵上所有满足 $Φ(ABA)=Φ(A)Φ(B)Φ(A)$ 的Jordan三重积同态映射。
The Nearest Hermitian Inverse Eigenvalue Problem Solution with Respect to the 2-Norm
本文研究在给定埃尔米特矩阵的特征值和给定埃尔米特矩阵的情况下，如何找到最接近给定算子的埃尔米特矩阵，通过随机矩阵和灰度图像测试其平滑特性。
In this paper we extend DDVV-type inequalities involving the Frobenius norm of commutators from real symmetric and skew-symmetric matrices to Hermitian and skew-Hermitian matrices.
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 study the Rayleigh quotient of a Hermitian matrix with quaternionic coefficients and prove its main properties. As an application, we give some relationships between left and right eigenvalues of Hermitian and symplectic matrices.
The main purpose of this paper is to englobe some new and known types of Hermitian block-matrices $M=\begin{pmatrix} A \& X\\ {X^*} \& B\end{pmatrix}$ satisfying or not the inequality $\|M\|\le \|A+B\|$ for all symmetric norms
Jordan triple product homomorphisms on Hermitian matrices to and from dimension one
本文完整刻画了n×n复厄米矩阵与一维数域（复数、实数、非负实数）之间两个方向上的所有Jordan三重积同态映射。
Horn's conjecture, which given the spectra of two Hermitian matrices describes the possible spectra of the sum, was recently settled in the affirmative. In this survey we discuss one of the many steps in this, which required us to introduce a combinatorial gadget called a {\em honeycomb}; the question is then reformulable as about the existence of honeycombs with certain boundary conditions. Another important tool is the connection to the representation theory of the group U(n), by ``classical vs. quantum'' analogies.
Aggregate Bounds on the eigenvalues of the principal submatrices of a Hermitian matrix and majorization relations
本文扩展了Thompson关于Hermitian矩阵主子矩阵特征值和的界，并利用该结果推导出所有主子矩阵特征值之间的主导关系，涵盖Schur和Szasz的已有结果。
Perturbed Block Toeplitz matrices and the non-Hermitian skin effect in dimer systems of subwavelength resonators
该研究推导扰动三对角块Toeplitz矩阵本征对显式公式，从数学上论证亚波长谐振器二聚体系统非厄米趋肤效应的存在、拓扑起源及异质结构界面模的局域化特性。
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