Pairs of matrices, one of which commutes with their commutator.
Pairs of Quadratic Forms.
Parallel and superfast algorithms for Hankel systems of equations.
Parallel QR Decomposition of a Rectangular Matrix.
Partial choice functions for families of finite sets
Let m ≥ 2 be an integer. We show that ZF + “Every countable set of m-element sets has an infinite partial choice function” is not strong enough to prove that every countable set of m-element sets has a choice function, answering an open question from . (Actually a slightly stronger result is obtained.) The independence result in the case where m = p is prime is obtained by way of a permutation (Fraenkel-Mostowski) model of ZFA, in which the set of atoms (urelements) has the structure of a vector...
Partial convergence and sign convergence of matrix powers via eigen c-ads.
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...