Related papers: Generalized even and odd totally positive matrices
The existence and construction of common invariant cones for families of real matrices is considered. The complete results are obtained for 2x2 matrices (with no additional restrictions) and for families of simultaneously diagonalizable…
We generalize the well known characterizations of totally nonnegative and oscillatory matrices, due to F.R.Gantmacher, M.G.Krein, A.Whitney, C.Loewner, M.Gasca, and J.M.Pena to the case of an arbitrary complex semisimple Lie group.
This paper is devoted to the generalization of the theory of total positivity. We say that a linear operator A in R^n is generalized totally positive (GTP), if its jth exterior power preserves a proper cone K_j in the corresponding space…
In this paper, two kinds of generalizations of ideal matrices, generalized ideal matrices and double ideal matrices. are obtained and studied, The concepts of generalized ideal matrices and double ideal matrices are proposed, and their…
In this paper, closed formulas for the eigenvectors of a particular class of matrices generated by generalized permutation matrices, named generalized circulant matrices, are presented.
In this paper, we introduce two types of general classes of even and odd $q$-Lidstone polynomial sequences. We prove essential properties related to them like the matrix and determinate form representation, the generating function,…
In this note a general result is proved that can be used to evaluate exactly a class of highly oscillatory integrals.
The concept of double nonnegativity of matrices is generalized to doubly nonnegative tensors by means of the nonnegativity of all entries and $H$-eigenvalues. This generalization is defined for tensors of any order (even or odd), while it…
Sturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. What we propose here is a Sturm oscillation theorem for systems of…
The paper develops the general theory for the items in the title, assuming that the matrix is countable and cofinal.
In this note, we present a generalization of some results concerning the spectral properties of a certain class of block matrices. As applications, we study some of its implications on nonnegative matrices, doubly stochastic matrices and…
We derived the sum identities for generalized harmonic and corresponding oscillatory numbers for which a sieve procedure can be applied. The obtained results enable us to understand better the properties of these numbers and their…
In this paper, eventually totally positive matrices (i.e. matrices all whose powers starting with some point are totally positive) are studied. We present a new approach to eventual total positivity which is based on the theory of…
This article represents a major step in the unification of the theory of algebraic, topological and singular transition matrices by introducing a definition which is a generalization that encompasses all of the previous three. When this…
We show that any connected regular graph with $d+1$ distinct eigenvalues and odd-girth $2d+1$ is distance-regular, and in particular that it is a generalized odd graph.
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
Positive real odd matrix functions, often referred to as positive real lossless matrix functions, play an important role in many applications in multi-port electrical systems. In this paper we present closer analogues to some of the known…
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…
The congruence orbit of a matrix has a natural connection with the linear complementarity problem on simplicial cones formulated for the matrix. In terms of the two approaches -- the congruence orbit and the family of all simplicial cones…
Copositive and completely positive matrices play an increasingly important role in Applied Mathematics, namely as a key concept for approximating NP-hard optimization problems. The cone of copositive matrices of a given order and the cone…