-adic Clifford algebras
-matrices and Lyapunov scalar stability.
Paare alternierender Formen.
Pairs of Clifford algebras of the Hurwitz type
For a given Hurwitz pair the existence of a bilinear mapping (where and ) denote the Clifford algebras of the quadratic forms and , respectively) generated by the Hurwitz multiplication “o” is proved and the counterpart of the Hurwitz condition on the Clifford algebra level is found. Moreover, a necessary and sufficient condition for "⭑" to be generated by the Hurwitz multiplication is shown.
Pairs of k -step reachability and m -step observability matrices
Let V and W be matrices of size n × pk and qm × n, respectively. A necessary and sufficient condition is given for the existence of a triple (A,B,C) such that V a k-step reachability matrix of (A,B) andW an m-step observability matrix of (A,C).
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.