深入解析：厄米特矩阵的世界在复数领域中，厄米特矩阵（Hermitian Matrix），又称埃尔米特矩阵或厄米矩阵，是一种特殊类型的矩阵，其独特的性质赋予了它们在物理和工程学中的重要地位。它的定义要求矩阵中任意元素 (i, j) 的共轭与 (j, i) 的元素相等，即 Aji = Aij*，其中星号表示共轭。对于复向量...
Is a Matrix Hermitian?Robin K. S. Hankin
A modern interpretation of the Dirac-electron continuity equation For a non-Hermitian matrix A = [([a.sub.ij]).sub.N x N] [member of] [C.sup.N x N], theHermitian conjugateof A is denoted as Exploiting the composite step strategy to the biconjugate, A-orthogonal residual method for ...
It is well known that the average distribution of eigenvalues of a matrix, whose elements have a Gaussian distribution, may be determined. Here it is shown that the sum of such a matrix with a non-fluctuating matrix can also be resolved, in as much as the problem can be reduced to the...
We prove that any Hermitian matrix whose trace is integer and all eigenvalues lie in the segment [1 + 1/(k 3),k 1 1/(k 3)] can be represented as a sum of k orthogonal projections. For the sums of k orthogonal projections, it is shown that the ratio of the number of eigenvalues...
Furthermore, we give bounds on the Hermitian-Randi energy of a general mixed graph. Finally, we give some results about the Hermitian-Randi energy of mixed trees. 展开 关键词: mixed graph Hermitian-adjacency matrix Hermitian-Randić matrix Hermitian-Randić energy ...
Here \\(\\mathcal{D}_{p}\\) is defined by the inequality \\(\\|\\mathrm{P}(z)\\|\\;<\\;1\\) , where \\(\\mathrm{P}(z)\\) is a direct sum of matrix polynomials \\(\\mathrm{P_i}(z)\\) (so that an appropriate Archimedean condition is satisfied), and \\(\\mathr...
Sa, The inertia of a Hermitian matrix having prescribed complementary principal submatrices, Linear Algebra Appl. 37 (1981) 161-171.B. E. Cain and E. Marques de S~, The inertia of a Hermitian matrix having prescribed complementary principal submatrices, Linear Algebra Appl. 37:161-171 (1981)...
内容提示: arXiv:1811.05854v2 [math.NA] 16 Nov 2018When is a matrix unitary or Hermitian plus low rank? ∗Gianna M. Del Corso, Federico Poloni, Leonardo Robol, andRaf Vandebril †November 28, 2018AbstractHermitian and unitary matrices are two representatives of the class of normal matrices...
The paper gives a thorough introduction to spectra of digraphs via its Hermitian adjacency matrix. This matrix is indexed by the vertices of the digraph, and the entry corresponding to an arc from $x$ to $y$ is equal to the complex unity $i$ (and its symmetric entry is $-i$) if the...