Explicit Solutions of some Linear Matrix Equations
Exploiting tensor rank-one decomposition in probabilistic inference
We propose a new additive decomposition of probability tables – tensor rank-one decomposition. The basic idea is to decompose a probability table into a series of tables, such that the table that is the sum of the series is equal to the original table. Each table in the series has the same domain as the original table but can be expressed as a product of one- dimensional tables. Entries in tables are allowed to be any real number, i. e. they can be also negative numbers. The possibility of having...
Exponential polynomial inequalities and monomial sum inequalities in -Newton sequences
We consider inequalities between sums of monomials that hold for all p-Newton sequences. This continues recent work in which inequalities between sums of two, two-term monomials were combinatorially characterized (via the indices involved). Our focus is on the case of sums of three, two-term monomials, but this is very much more complicated. We develop and use a theory of exponential polynomial inequalities to give a sufficient condition for general monomial sum inequalities, and use the sufficient...
Exponential Riordan arrays and permutation enumeration.
Exponents of two-colored digraphs
We consider the primitive two-colored digraphs whose uncolored digraph has vertices and consists of one -cycle and one -cycle. We give bounds on the exponents and characterizations of extremal two-colored digraphs.
Expression de comme quotient de deux déterminants
Expression of a tensor commutation matrix in terms of the generalized Gell-Mann matrices.
Extension and generalization inequalities involving the Khatri-Rao product of several.
Extension de la méthode Procuste à la comparaison de nuages de points situés dans des espaces de dimensions différentes
Extension of -dimensional Euclidean vector space over to pseudo-fuzzy vector space over .
Extension of Partial Diagonals of Matrices I.
Extension of Partial Diagonals of Matrices II.
Extension of Wang-Gong monotonicity result in semisimple Lie groups
We extend a monotonicity result of Wang and Gong on the product of positive definite matrices in the context of semisimple Lie groups. A similar result on singular values is also obtained.
Extensions of the Graham-Leeb-Rothschild theorem.
Extensions of the Minkowski determinant theorem
Extensions of Three Matrix Inequalities to Semisimple Lie Groups
We give extensions of inequalities of Araki-Lieb-Thirring, Audenaert, and Simon, in the context of semisimple Lie groups.
Exterior Algebra and Projections of Polytopes.
Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems
Recently, Na Huang and Changfeng Ma in (2016) proposed two kinds of typical practical choices of the PPS method. In this paper, we extrapolate two versions of the PPS iterative method, and we introduce the extrapolated Hermitian and skew-Hermitian positive definite and positive semi-definite splitting (EHPPS) iterative method and extrapolated triangular positive definite and positive semi-definite splitting (ETPPS) iterative method. We also investigate convergence analysis and consistency of the...
Extremal algebraic connectivities of certain caterpillar classes and symmetric caterpillars.
Extremal inverse eigenvalue problem for matrices described by a connected unicyclic graph
In this paper, we deal with the construction of symmetric matrix whose corresponding graph is connected and unicyclic using some pre-assigned spectral data. Spectral data for the problem consist of the smallest and the largest eigenvalues of each leading principal submatrices. Inverse eigenvalue problem (IEP) with this set of spectral data is generally known as the extremal IEP. We use a standard scheme of labeling the vertices of the graph, which helps in getting a simple relation between the characteristic...