On weighted partial orderings on the set of rectangular complex matrices.
On -extremal non-regular graphs.
One-sided simultaneous inequalities and sandwich theorems for diagonal similarity and diagonal equivalence of nonnegative matrices.
Operator norms of words formed from positive-definite matrices.
Orbit measures, random matrix theory and interlaced determinantal processes
A connection between representation of compact groups and some invariant ensembles of hermitian matrices is described. We focus on two types of invariant ensembles which extend the gaussian and the Laguerre Unitary ensembles. We study them using projections and convolutions of invariant probability measures on adjoint orbits of a compact Lie group. These measures are described by semiclassical approximation involving tensor and restriction multiplicities. We show that a large class of them are determinantal....
Orders in quaternion algebras.
Orders of some modular linear groups.
Orthogonal diagonalization for complex skew-persymmetric anti-tridiagonal Hankel matrices
In this paper, we obtain an eigenvalue decomposition for any complex skew-persymmetric anti-tridiagonal Hankel matrix where the eigenvector matrix is orthogonal.
Orthogonal polynomial ensembles in probability theory.
Overlapping Pfaffians.
-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.