Subspaces of symmetric matrices containing matrices with a multiple first eigenvalue

Properties of Central Symmetric X-Form Matrices

In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.

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...

On symmetric matrices with exactly one positive eigenvalue

On the nonnegative inverse eigenvalue problem of traditional matrices

In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.

Neutral subspaces of pairs of symmetric/skewsymmetric real matrices

Let A and B be n × n real matrices with A symmetric and B skewsymmetric. Obviously, every simultaneously neutral subspace for the pair (A,B) is neutral for each Hermitian matrix X of the form X = μA + iλB, where μ and λ are arbitrary real numbers. It is well-known that the dimension of each neutral subspace of X is at most In+(X) + In0(X), and similarly, the dimension of each neutral subspace o...