Ranks and independence of solutions of the matrix equation .
Ranks of permutative matrices
A new type of matrix, termed permutative, is defined and motivated herein. The focus is upon identifying circumstances under which square permutative matrices are rank deficient. Two distinct ways, along with variants upon them are given. These are a special kind of grouping of rows and a type of partition in which the blocks are again permutative. Other, results are given, along with some questions and conjectures.
Rational algebra and MM functions
MM functions, formed by finite composition of the operators min, max and translation, represent discrete-event systems involving disjunction, conjunction and delay. The paper shows how they may be formulated as homogeneous rational algebraic functions of degree one, over (max, +) algebra, and reviews the properties of such homogeneous functions, illustrated by some orbit-stability problems.
Rational orthogonal versus real orthogonal.
Rational realization of the minimum ranks of nonnegative sign pattern matrices
A sign pattern matrix (or nonnegative sign pattern matrix) is a matrix whose entries are from the set (, respectively). The minimum rank (or rational minimum rank) of a sign pattern matrix is the minimum of the ranks of the matrices (rational matrices, respectively) whose entries have signs equal to the corresponding entries of . Using a correspondence between sign patterns with minimum rank and point-hyperplane configurations in and Steinitz’s theorem on the rational realizability of...
Rayon de la sphère circonscrite au tétraèdre en fonction des arêtes
Reachability and observability of linear systems over max-plus
This paper discusses the properties of reachability and observability for linear systems over the max-plus algebra. Working in the event-domain, the concept of asticity is used to develop conditions for weak reachability and weak observability. In the reachability problem, residuation is used to determine if a state is reachable and to generate the required control sequence to reach it. In the observability problem, residuation is used to estimate the state. Finally, as in the continuous-variable...
Reachability indices of positive linear systems.
Reachability matrices and cyclic matrices.
Real closures of commutative rings. II.
Real equivalence of complex matrix pencils and complex projections of real Segre varieties.
Real linear matrix analysis
Real vector space with scalar product of quasi-triangular fuzzy numbers.
Recent trends on analytic properties of matrix orthonormal polynomials.
Recherches analytiques sur la surface du troisième ordre qui est la réciproque de la surface de Steiner
Recognition of hidden positive row diagonally dominant matrices.
Recounting determinants for a class of Hessenberg matrices.
Rectangular Scott-type permanents.
Rectification : «Algèbres de Clifford symplectiques et revêtements spinoriels du groupe symplectique»
Reducing the adjacency matrix of a tree.