-matrices and Lyapunov scalar stability.
Partial transposes of permutation matrices.
Path counting and random matrix theory.
Path product and inverse M-matrices.
Paths of matrices with the strong Perron-Frobenius property converging to a given matrix with the Perron-Frobenius property.
Patterns with several multiple eigenvalues
Identified are certain special periodic diagonal matrices that have a predictable number of paired eigenvalues. Since certain symmetric Toeplitz matrices are special cases, those that have several multiple 5 eigenvalues are also investigated further. This work generalizes earlier work on response matrices from circularly symmetric models.
Pentadiagonal Companion Matrices
The class of sparse companion matrices was recently characterized in terms of unit Hessenberg matrices. We determine which sparse companion matrices have the lowest bandwidth, that is, we characterize which sparse companion matrices are permutationally similar to a pentadiagonal matrix and describe how to find the permutation involved. In the process, we determine which of the Fiedler companion matrices are permutationally similar to a pentadiagonal matrix. We also describe how to find a Fiedler...
Perfect sampling from the limit of deterministic products of stochastic matrices.
Perimeter preserver of matrices over semifields
For a rank- matrix , we define the perimeter of as the number of nonzero entries in both and . We characterize the linear operators which preserve the rank and perimeter of rank- matrices over semifields. That is, a linear operator preserves the rank and perimeter of rank- matrices over semifields if and only if it has the form , or with some invertible matrices U and V.
Permanental associated matrices and Schneider's theorem.
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.