The graph of Hermitian-adjacency matrix is a mixed graph consisting adjacency matrix ofan undirected graph and skew-adjacency matrix of a digraph. In this paper we discuss eigenvalues ofHermitian-adjacency matrix. Then we use the eigenvalues to determine the possible Hamiltoniancycles of its graph....
Hermitian matrixrank-one modificationSUMMARYIn this paper, we present some new interlacing properties about the bounds of the eigenvalues for rank-one modification of Hermitian matrix, whose eigenvalues are different and spectral decomposition also needs to be known. Numerical examples demonstrate the ...
With this method, we can form Hermitian, anti-Hermitian, symmetric and general matrices with arbitrary eigenvalues with great ease. Certain functions are required for the implementation of this method. Probability amplitudes connecting observables with discrete eigenvalue spectra perform the task, and ...
For commutingHermitianmatrices, there is a unitary matrixUthat jointly diagonalizes all matrices. For this significantly simpler situation, compared to the general non-Hermitian case, randomized methods based on (2) have recently been analyzed in [18], establishing favorable robustness and stability pr...
These subroutines compute eigenvalues, and optionally, the eigenvectors of a real symmetric band matrix or a complex Hermitian band matrix: SSBEV and DSBEV compute all eigenvalues, and optionally, the eigenvectors of real symmetric band matrix A, stored in ...
We introduce the normalized adjacency matrix (1.1) where the normalization is chosen so that the eigenvalues of A are typically of order one. The goal of this paper is to obtain the asymptotic distribution of the extreme eigenvalues of A. The extreme eigenvalues of graphs are of fundamental ...
By means of the properties of the Hermitian-Antireflexive matrix,the least-square solution of the left and right inverse eigenvalue problem of Hermitian-Antireflexive matrix is derived and the necessary and sufficient conditions of the problem are considered and then the general expression of the so...
matrix elementsoptical spectraIt is shown that the eigenvalues E i of a Hermitian matrix H with matrix elements H ij = 危 k A k ij a k, where A k ij are known numbers and a k a set of parameters, can be exactly expanded as E i = 危 k( E i a k)a k. This property is ...
We derive an algorithm based on the boundedness of these second derivatives for the global minimization of an eigenvalue of an analytic Hermitian matrix function. The algorithm is globally convergent. It determines the globally minimal value of a piece-wise quadratic under-estimator for the eigen...
Asymptotic growth rates are obtained for the eigenvalues of a partitioned Hermitian matrix having positive definite and negative definite complementary principal submatrices, when the nonprincipal submatrix grows indefinitely large.doi:10.1016/0024-3795(74)90041-XR.C. Thom...