Results 11 to 20 of about 169 (28)

Lectures on the Routh-Hurwitz problem [PDF]

arXiv, 2008
The notes contain a streamlined account on stability of univariate polynomials and related ...
arxiv  

From totally nonnegative matrices to quantum matrices and back, via Poisson geometry [PDF]

arXiv, 2009
In this survey article, we describe recent work that connects three separate objects of interest: totally nonnegative matrices; quantum matrices; and matrix Poisson varieties.
arxiv  

The Lukács--Olkin--Rubin theorem on symmetric cones [PDF]

arXiv, 2013
In this paper we prove a Luk\'{a}cs type characterization theorem of the Wishart distribution on Euclidean simple Jordan algebras under weak regularity assumptions (e.g. measurability) on the densities.
arxiv  

On positive bivariate quartic forms [PDF]

arXiv, 2015
A bivariate quartic form is a homogeneous bivariate polynomial of degree four. A criterion of positivity for such a form is known. In the present paper this criterion is reformulated in terms of pseudotensorial invariants of the form.
arxiv  

Totally nonnegative and oscillatory elements in semisimple groups [PDF]

arXiv, 1998
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.
arxiv  

Loop-erased walks and total positivity [PDF]

arXiv, 2000
We consider matrices whose elements enumerate weights of walks in planar directed weighted graphs (not necessarily acyclic). These matrices are totally nonnegative; more precisely, all their minors are formal power series in edge weights with nonnegative coefficients.
arxiv  

Theorems and counterexamples on structured matrices [PDF]

arXiv, 2005
The subject of Chapter 1 is GKK $\tau$-matrices and related topics. Chapter 2 is devoted to boundedly invertible collections of matrices, with applications to operator norms and spline approximation. Various structured matrices (Toeplitz, Hessenberg, Hankel, Cauchy, and other) are used extensively throughout the thesis.
arxiv  

M-matrices satisfy Newton's inequalities [PDF]

Proc. Amer. Math. Soc. 133 (2005), 711-717, 2005
Newton's inequalities $c_n^2 \ge c_{n-1}c_{n+1}$ are shown to hold for the normalized coefficients $c_n$ of the characteristic polynomial of any $M$- or inverse $M$-matrix. They are derived by establishing first an auxiliary set of inequalities also valid for both of these classes.
arxiv  

Universal algorithms for generalized discrete matrix Bellman equations with symmetric Toeplitz matrix [PDF]

Tambov Univ. Reports, ser. Natural and Technical Sciences, 16(6, part 2), 2011, 1751-1758, 2006
This paper presents two universal algorithms for generalized Bellman equations with symmetric Toeplitz matrix. The algorithms are semiring extensions of two well-known methods solving Toeplitz systems in the ordinary linear algebra.
arxiv  

On common invariant cones for families of matrices [PDF]

arXiv, 2009
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 matrices of any size.
arxiv