Polynomial numerical hulls of order 3.
Polynomial Riccati equations with algebraic solutions
We consider the equations of the form dy/dx = y²-P(x) where P are polynomials. We characterize the possible algebraic solutions and the class of equations having such solutions. We present formulas for first integrals of rational Riccati equations with an algebraic solution. We also present a relation between the problem of algebraic solutions and the theory of random matrices.
Polynomial sequences generated by infinite Hessenberg matrices
We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz...
Polynomials and linear transformations over finite fields.
Positive 2D discrete-time linear Lyapunov systems
Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.
Positive definiteness of tridiagonal matrices via the numerical range.
Positive eigenvalues and two-letter generalized words.
Positive semidefinite matrices, exponential convexity for majorization, and related Cauchy means.
Positive semidefiniteness of estimated covariance matrices in linear models for sample survey data
Descriptive analysis of sample survey data estimates means, totals and their variances in a design framework. When analysis is extended to linear models, the standard design-based method for regression parameters includes inverse selection probabilities as weights, ignoring the joint selection probabilities. When joint selection probabilities are included to improve estimation, and the error covariance is not a diagonal matrix, the unbiased sample based estimator of the covariance is the Hadamard...
Positive splittings of matrices and their nonnegative Moore-Penrose inverses
In this short note we study necessary and sufficient conditions for the nonnegativity of the Moore-Penrose inverse of a real matrix in terms of certain spectral property shared by all positive splittings of the given matrix.
Positivity and stabilization of 2D linear systems
The problem of finding a gain matrix of the state-feedback of 2D linear system such that the closed-loop system is positive and asymptotically stable is formulated and solved. Necessary and sufficient conditions for the solvability of the problem are established. It is shown that the problem can be reduced to suitable linear programming problem. The proposed approach can be extended to 2D linear system described by the 2D Roesser model.
Positivity in Complex Spaces and Its Application to Gershgorin Discs.
Positivity with Respect to the Round Cone
Possible isolation number of a matrix over nonnegative integers
Let be the semiring of all nonnegative integers and an matrix over . The rank of is the smallest such that can be factored as an matrix times a matrix. The isolation number of is the maximum number of nonzero entries in such that no two are in any row or any column, and no two are in a submatrix of all nonzero entries. We have that the isolation number of is a lower bound of the rank of . For with isolation number , we investigate the possible values of the rank of ...
Power indices of trace zero symmetric Boolean matrices
The power index of a square Boolean matrix A is the least integer d such that Ad is a linear combination of previous nonnegative powers of A. We determine the maximum power indices for the class of n×n primitive symmetric Boolean matrices of trace zero, the class of n×n irreducible nonprimitive symmetric Boolean matrices, and the class of n×n reducible symmetric Boolean matrices of trace zero, and characterize the extreme matrices respectively.
Problème des moments matriciels sur la droite : construction d'une famille de solutions et questions d'unicité
Product of exponentials and spectral radius of random k-circulants
We consider n × n random k-circulant matrices with n → ∞ and k = k(n) whose input sequence {al}l≥0 is independent and identically distributed (i.i.d.) random variables with finite (2 + δ) moment. We study the asymptotic distribution of the spectral radius, when n = kg + 1. For this, we first derive the tail behaviour of the g fold product of i.i.d. exponential random variables. Then using this tail behaviour result and appropriate normal approximation techniques, we show that with appropriate scaling...
Product of range symmetric block matrices in Minkowski space.
Products of Infinite-Dimensional Non-Negative Matrices; Extension of Hajnal's Results.
Products of -matrices and nested sequences of principal minors.