Random matrices and permutations, matrix integrals and integrable systems
Random matrices, magic squares and matching polynomials.
Random matrices, non-colliding processes and queues
Random walk centrality and a partition of Kemeny's constant
We consider an accessibility index for the states of a discrete-time, ergodic, homogeneous Markov chain on a finite state space; this index is naturally associated with the random walk centrality introduced by Noh and Reiger (2004) for a random walk on a connected graph. We observe that the vector of accessibility indices provides a partition of Kemeny's constant for the Markov chain. We provide three characterizations of this accessibility index: one in terms of the first return time to the state...
Range symmetric matrices in Minkowski space.
Rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix.
Rank and perimeter preserver of rank-1 matrices over max algebra
For a rank-1 matrix over max algebra, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the linear operators which preserve the rank and perimeter of rank-1 matrices over max algebra. That is, a linear operator T preserves the rank and perimeter of rank-1 matrices if and only if it has the form T(A) = U ⊗ A ⊗ V, or with some monomial matrices U and V.
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.
Rate of convergence to the semi-circle law for the Deformed Gaussian Unitary Ensemble
It is shown that the Kolmogorov distance between the expected spectral distribution function of an n × n matrix from the Deformed Gaussian Ensemble and the distribution function of the semi-circle law is of order O(n −2/3+v ).
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...
Reachability indices of positive linear systems.
Reachability of cone fractional continuous-time linear systems
A new class of cone fractional continuous-time linear systems is introduced. Necessary and sufficient conditions for a fractional linear system to be a cone fractional one are established. Sufficient conditions for the reachability of cone fractional systems are given. The discussion is illustrated with an example of linear cone fractional systems.
Recherche de la dimension de l'espace latent en ACP
Recognition of hidden positive row diagonally dominant matrices.
Reduction to normal form of a self-adjoint linear transformation with respect to a pseudo-unitary or a pseudo-Euclidean inner product.
Refined counting of fully packed loop configurations.
Refined inertially and spectrally arbitrary zero-nonzero patterns.
Regions containing eigenvalues of a matrix.
Regular Simplices and Gaussian Samples.