Related papers: New properties for certain positive semidefinite m…
In this paper, we establish several new inequalities for twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.
It is known that semi-magic square matrices form a 2-graded algebra or superalgebra with the even and odd subspaces under centre-point reflection symmetry as the two components. We show that other symmetries which have been studied for…
A unified treatment of both superconformal and quasisuperconformal algebras with quadratic non-linearity is given. General formulas describing their structure are found by solving the Jacobi identities. A complete classification of…
We present a criterion, based on three commutator relations, that allows to decide whether two self-adjoint matrices with non-overlapping support are simultaneously unitarily similar to quasidiagonal matrices, i.e., whether they can be…
In this short note, we show some inequalities on Cartan matrices, centers and socles of blocks of group algebras. Our main theorems are generalizations of the facts on dimension of Reynolds ideals.
The "2-variable general-$\lambda$-matrix polynomials (2VG$\lambda$MP)" is a new family of matrix polynomials, introduced and studied in this article. These matrix polynomials are constructed using umbral and symbolic methods. We delve into…
Several new verifiable conditions are established for block matrices with scalar diagonal blocks to have the numerical range equal the convex hull of at most k ellipses where k by k is the size of the smaller diagonal block. For k = 2,…
We consider the alternating sign matrices of the odd order that have some kind of central symmetry. Namely, we deal with matrices invariant under the half-turn, quarter-turn and flips in both diagonals. In all these cases, there are two…
We consider graphs for which the non-backtracking matrix has defective eigenvalues, or graphs for which the matrix does not have a full set of eigenvectors. The existence of these values results in Jordan blocks of size greater than one,…
A description of the endomorphisms of semidirect products of two groups as a group of $2\times 2$ matrices of maps is already known. Using this description, we have studied the concept of determinant for the endomorphisms of semidirect…
We compute the asymptotics of eigenvalues of Jacobi matrices with the zero coefficients on the main diagonal and the off-diagonal coefficients which converge to zero.
The main purpose of this paper is, in the general setting of the adjointable operators on Hilbert $C^*$-modules, to develop two new tools that can be applied to deal with the positive solutions of certain operator equations, the operator…
A well-known fact in linear algebra is that $A^T A$ is always positive semi-definite for any real matrix $A$. We consider a generalization of this fact via the following decision problem. Given a symbolic product of length $k$, consisting…
We study the diagonals of two-dimensional tilings generated by direct product substitutions. The properties of these diagonals are primarily determined by the eigenvalues of the substitution matrix, but also the order of the letters in the…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
The nonlinear eigenvalue problem of a class of second order semi-transcendental differential equations is studied. A nonlinear eigenvalue is defined as the initial condition which gives rise a separatrix solution. A semi-transcendental…
In this paper, we describe the structural properties of the cone of $\mathcal{Z}$-transformations on the second order cone in terms of the semidefinite cone and copositive/completely positive cones induced by the second order cone and its…
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying…
In this paper new criteria are established for the existence of positive radial solutions of a semilinear elliptic system depending on the gradient. These criteria are determined by some relationships between the upper and lower bounds on…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…