Orthogonal designs II.
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 Groups of Dyadic Unimodular Quadratic Forms.
Orthogonal polynomial ensembles in probability theory.
Orthogonality and complementation in the lattice of subspaces of a finite vector space
We investigate the lattice of subspaces of an -dimensional vector space over a finite field with a prime power together with the unary operation of orthogonality. It is well-known that this lattice is modular and that the orthogonality is an antitone involution. The lattice satisfies the chain condition and we determine the number of covers of its elements, especially the number of its atoms. We characterize when orthogonality is a complementation and hence when is orthomodular. For...
Orthogonality of immanants
Orthogonality-preserving transformations on quadratic spaces
Orthogonalization, factorization, and identification as to the theory of recursive equations in linear algebra.
Overlapping Pfaffians.
-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.