A min-max theorem for complex symmetric matrices

We optimize the form Re x^tTx to obtain the singular values of a complex symmetric matrix T. We prove that for ,

     

Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices

Let be the set of entrywise nonnegative n×n matrices. Denote by r(A) the spectral radius (Perron root) of . Characterization is obtained for maps such that r(f(A)+f(B))=r(A+B) for all . In particular, it is shown that such a map has the form

     

Interior estimates for solutions of a fourth order nonlinear partial differential equation

Let be a locally strongly convex hypersurface, given by the graph of a convex function xn+1=f(x₁,…,xn) defined in a convex domain Ω⊂Rn. M is called a α-extremal hypersurface, if f is a solution of

     

On eigenvalues of meet and join matrices associated with incidence functions

Let (P,?,∧) be a locally finite meet semilattice. Let

     

A norm compression inequality for block partitioned positive semidefinite matrices

Let A be a positive semidefinite matrix, block partitioned as

     

On the max version of the generalized spectral radius theorem

Let Ψ be a bounded set of n×n non-negative matrices. Recently, the max algebra version μ(Ψ) of the generalized spectral radius of Ψ was introduced. We show that

     

Numerical ranges of weighted shift matrices with periodic weights

Let A be an n-by-n (n?2) matrix of the form

     

Young’s inequality and trace

Let φ be a positive linear functional on M_n(C) and f,g mutually conjugate in the sense of Young. In this note we show a necessary and sufficient condition for the inequality

     

Identities for sums of characteristic values of entire matrix pencils

The paper deals with an entire matrix-valued function of a complex argument (an entire matrix pencil) f of order ρ(f)<∞. Identities for the following sums of the characteristic values of f are established:

     

On the continuity of the generalized spectral radius in max algebra

Given a bounded set Ψ of n×n non-negative matrices, let ρ(Ψ) and μ(Ψ) denote the generalized spectral radius of Ψ and its max version, respectively. We show that

     

Commutators with maximal Frobenius norm

It is known that for any nonzero complex n×n matrices X and Y the quotient of Frobenius norms

     

Numerical ranges of weighted shift matrices

We show that if A is an n-by-n (n?3) matrix of the form

     

Extension of Rotfel’d Theorem

Let f(t) be a non-negative concave function on the positive half-line. Given an arbitrary partitioned positive semi-definite matrix, we show that

     

A convergence analysis of block accelerated over-relaxation iterative methods for weak block H-matrices to partition π

The aim of this paper is to establish the convergence of the block iteration methods such as the block successively accelerated over-relaxation method (BAOR) and the symmetric block successively accelerated over-relaxation method (BSAOR): Let be a weak block H-matrix to partition π, then for ,

     

Flat portions on the boundary of the Davis-Wielandt shell of 3-by-3 matrices

Let T be an n×n matrix. The Davis-Wielandt shell of T is defined as the set

     

On upper bounds for Laplacian graph eigenvalues

In this paper, we obtain the following upper bound for the largest Laplacian graph eigenvalue λ(G):

     

A Dunkl-Williams type inequality for absolute value operators

Dunkl and Williams showed that for any nonzero elements x,y in a normed linear space X

     

Inverse eigenvalue problems for linear complementarity systems

Traditionally an inverse eigenvalue problem is about reconstructing a matrix from a given spectral data. In this work we study the set of real matrices A of order n such that the linear complementarity system

     

Existence theory for positive solutions to one-dimensional p-Laplacian boundary value problems on time scales

In this paper we consider the one-dimensional p-Laplacian boundary value problem on time scales