Showing papers on "Spectrum of a matrix published in 2022"
1 citations
TL;DR: In this paper , the Aα-eigenvalues of a simple graph of order n were studied under vertex deletion, vertex contraction, edge deletion, edge subdivision and edge subdivision.
Abstract: Let G be a simple graph of order n. For α∈[0,1], the Aα-matrix of G is defined as Aα(G)=αD(G)+(1−α)A(G), where A(G) and D(G) are the adjacency matrix and the diagonal degree matrix of G, respectively. The eigenvalues of the Aα-matrix of G are called the Aα-eigenvalues of G. In this paper, we first study the properties on Aα-eigenvalues, i.e. how the Aα-eigenvalues behave under some kinds of graph transformations including vertex deletion, vertex contraction, edge deletion and edge subdivision. Moreover, we also present the relationships between the Aα-eigenvalues of G and its k-domination number, independence number, chromatic number and circumference, respectively.
10 Nov 2022
TL;DR: In this article , the intelligent application of matrix eigenvalues and eigenvalue methods based on tensor analysis is studied, in order for students to have a deep understanding of eigen values and Eigenvectors from multiple perspectives.
Abstract: This paper firstly studies the intelligent application of matrix eigenvalues and eigenvalue methods based on tensor analysis. Then, starting from the concept of eigenvalues and eigenvectors and the eigenvalue decomposition theorem, through intuitive geometric demonstration, eigenvalue deployment and high-dimensional data Two specific examples of dimensionality reduction, combined with MATLAB software to clarify the geometric intuition and practical application of eigenvalues and eigenvectors, in order for students to have a deep understanding of eigenvalues and eigenvectors from multiple perspectives.
12 Oct 2022
TL;DR: In this paper , the eigenvalues and eigenvectors of the bicomplex matrix were investigated, and their properties were established, and some results on the Eigenvalues of some special BICOMplex matrices were established.
Abstract: In this paper, we studied eigenvalues and eigenvectors of the bicomplex matrix, investigated their properties, and established some results. We have also established some results on the eigenvalues of some special bicomplex matrices.
TL;DR: In this article , the authors find a nearest matrix from the set of complex matrices X ? Cm?m to matrix D (with respect to spectral norm) such that the matrix A B C X ! has two prescribed eigenvalues ?1 and ?2.
Abstract: Given four complex matrices A, B, C and D where A ? Cn?n and D ? Cm?m and
given two distinct arbitrary complex numbers ?1 and ?2, so that they are not
eigenvalues of the matrix A, we find a nearest matrix from the set of
matrices X ? Cm?m to matrix D (with respect to spectral norm) such that
the matrix A B C X ! has two prescribed eigenvalues ?1 and ?2.
01 Jan 2022
TL;DR: In this article , the analysis of the stability of dynamic equilibria has been studied in the context of eigenvalues and eigenvectors, and it has been shown that eigenvalue analysis is among the most important applications of Eigenvalues.
Abstract: In the upcoming chapters, we will think about computing eigenvalues and eigenvectors. To explain why eigenvalues and eigenvectors are a useful thing to think about, I’ll devote one chapter to the analysis of the stability of dynamic equilibria. This is among the most important applications of eigenvalues.
28 Feb 2022
TL;DR: In this paper , the eigenvalues of the adjacency matrix of Cay(Z_n, S) and the anti-adjacency matrix (Cay(Z n, (Z n−{0})−S)−S ) were analyzed.
Abstract: In this paper, we give a relation between the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) and the eigenvalues of the antiadjacency matrix of Cay(Z_n, (Z_n−{0})−S), as well as the eigenvalues of the adjacency matrix of Cay(Z_n, S). Then, we give the characterization of connection set S where the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) are all integers.