Indefinite copositive matrices with exactly one positive eigenvalue or exactly one negative eigenvalue

Ela Indefinite Copositive Matrices with Exactly One Positive Eigenvalue or Exactly One Negative Eigenvalue

Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out if a matrix with exactly one negative eigenvalue is strictly copositive or not can be formulated ...

Ela on Symmetric Matrices with Exactly One Positive Eigenvalue

Abstract. We present a class of nonsingular matrices, the MC-matrices, and prove that the class of symmetric MC-matrices introduced by Shen, Huang and Jing [On inclusion and exclusion intervals for the real eigenvalues of real matrices. SIAM J. Matrix Anal. Appl., 31:816-830, 2009] and the class of symmetric MC-matrices are both subsets of the class of symmetric matrices with exactly one positi...

Eigenvalue analysis of constrained minimization problem for homogeneous polynomial

In this paper, the concepts of Pareto H -eigenvalue and Pareto Z -eigenvalue are introduced for studying constrained minimization problem and the necessary and sufficient conditions of such eigenvalues are given. It is proved that a symmetric tensor has at least one Pareto H -eigenvalue (Pareto Z -eigenvalue). Furthermore, theminimumPareto H -eigenvalue (or Pareto Z -eigenvalue) of a symmetric ...

On symmetric matrices with exactly one positive eigenvalue

The Main Eigenvalues of the Undirected Power Graph of a Group

The undirected power graph of a finite group $G$, $P(G)$, is a graph with the group elements of $G$ as vertices and two vertices are adjacent if and only if one of them is a power of the other. Let $A$ be an adjacency matrix of $P(G)$. An eigenvalue $lambda$ of $A$ is a main eigenvalue if the eigenspace $epsilon(lambda)$ has an eigenvector $X$ such that $X^{t}jjneq 0$, where $jj$ is the all-one...