Permanents – a concise survey. (Permanenten – Ein kurzer Überblick.)
Permanents of Hessenberg -matrices revisited.
Permanents of Hessenberg (0,1)-matrices.
Permutation matrices and matrix equivalence over a finite field.
Permutations without long decreasing subsequences and random matrices.
Perron complements of diagonally dominant matrices and H-matrices.
Perturbation of purely imaginary eigenvalues of Hamiltonian matrices under structured perturbations.
Perturbing non-real eigenvalues of nonnegative real matrices.
Poisson convergence for the largest eigenvalues of heavy tailed random matrices
We study the statistics of the largest eigenvalues of real symmetric and sample covariance matrices when the entries are heavy tailed. Extending the result obtained by Soshnikov in (Electron. Commun. Probab.9 (2004) 82–91), we prove that, in the absence of the fourth moment, the asymptotic behavior of the top eigenvalues is determined by the behavior of the largest entries of the matrix.
Poisson statistics for the largest eigenvalues of Wigner random matrices with heavy tails.
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.