Ela Inequalities for the Minimum Eigenvalue of M-matrices∗

Ela a New Eigenvalue Bound for the Hadamard Product of an M-matrix and an Inverse M-matrix

If A and B are n× n nonsingular M -matrices, a new lower bound for the minimum eigenvalue τ(A◦B) for the Hadamard product of A and B is derived. This bound improves the result of [R. Huang. Some inequalities for the Hadamard product and the Fan product of matrices. Linear Algebra Appl., 428:1551–1559, 2008.].

Several new inequalities for the minimum eigenvalue of M-matrices

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.

Further inequalities for operator space numerical radius on 2*2 operator ‎matrices

‎We present some inequalities for operator space numerical radius of $2times 2$ block matrices on the matrix space $mathcal{M}_n(X)$‎, ‎when $X$ is a numerical radius operator space‎. ‎These inequalities contain some upper and lower bounds for operator space numerical radius.

Some New Inequalities for Eigenvalues of the Hadamard Product and the Fan Product of Matrices

Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(A B) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M -matrices A and B are given. Some results of comparison are also given in theory. To illustrate ou...