Partial Derivations and B. Iversen's Linear Determinants.
Partial isometries and EP elements in rings with involution.
Partial sum of eigenvalues of random graphs
Let be a graph on vertices and let be the eigenvalues of its adjacency matrix. For random graphs we investigate the sum of eigenvalues , for , and show that a typical graph has , where is the number of edges of . We also show bounds for the sum of eigenvalues within a given range in terms of the number of edges. The approach for the proofs was first used in Rocha (2020) to bound the partial sum of eigenvalues of the Laplacian matrix.
Partial transposes of permutation matrices.
Particular trace decompositions and applications of trace decomposition to almost projective invariants
First, by using the formulae of Krupka, the trace decomposition for some particular classes of tensors of types (1, 2) and (1, 3) is obtained. Second, it is proved that the traceless part of a tensor is an almost projective invariant of weight 1. We apply this result to Weyl curvature tensors.
Partitionen und lineare Gleichungssysteme.
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 of commutativity: the commutant of the full pattern.
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.
p-dimensionale Vektoren modulo p. I. Zyklische Theorie.
Pencils of real symmetric matrices and the numerical range.
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.
Perimeter preservers of nonnegative integer matrices
We investigate the perimeter of nonnegative integer matrices. We also characterize the linear operators which preserve the rank and perimeter of nonnegative integer matrices. That is, a linear operator preserves the rank and perimeter of rank- matrices if and only if it has the form , or with appropriate permutation matrices and and positive integer matrix , where denotes Hadamard product.
Periodic coprime matrix fraction decompositions.
Periodicity in quasipolynomial convolution.
Periodické distribuce a diskrétní Fourierova transformace