Polynomials of the eigenvalues and powers of matrices
Polytopes secondaires et discriminants
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 definite solution of the matrix equation .
Positive definite solution of two kinds of nonlinear matrix equations.
Positive definiteness of tridiagonal matrices via the numerical range.
Positive eigenvalues and two-letter generalized words.
Positive entries of stable matrices.
Positive factors of Wythoff matrices.
Positive Matrix Functions on the Bitorus with Prescribed Fourier Coefficients in a Band.
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 stability of fractional descriptor time-varying discrete-time linear systems
The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor timevarying discrete-time linear systems. A method for computing solutions of fractional systems is proposed. Necessary and sufficient conditions for the positivity of these systems are established.
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 of operator-matrices of Hua-type.
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 bounded and exponentially bounded matrices
The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.