Počátkové nauky o determinantech. [III.]
Poincaré polynomials for unitary reflection groups.
Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils
Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils are addressed. Conditions for pointwise completeness and pointwise degeneracy of the systems are established and illustrated by an example.
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.
Pólya's permanent problem.
Polynomial eigenvalue problems with Hamiltonian structure.
Polynomial identities for hyper-matrices.
Polynomial identities for tensor products of Grassmann algebras.
Polynomial numerical hulls of order 3.
Polynomial operations: Numerical performance in matrix diophantine equation
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.
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.