Die neuere Algebra und die Ausdehnungslehre
Die Reduction linearer homogener Substitutionen von endlicher Periode auf ihre kanonische Form.
Diffeomorphisms of Rn with oscillatory jacobians.
The paper presents, mainly, two results: a new proof of the spectral properties of oscillatory matrices and a transversality theorem for diffeomorphisms of Rn with oscillatory jacobian at every point and such that NM(f(x) - f(y)) ≤ NM(x - y) for all elements x,y ∈ Rn, where NM(x) - 1 denotes the maximum number of sign changes in the components zi of z ∈ Rn, where all zi are non zero and z varies in a small neighborhood of x. An application to a semiimplicit discretization of the scalar heat equation...
Differencial equations for the analytic singular value decomposition of a matrix.
Digital image reconstruction in the spectral domain utilizing the Moore-Penrose inverse.
Dimension of non-Archimedean Banach spaces
Direct and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices
2000 Mathematics Subject Classification: 42C05.We give an easy procedure for solving of the direct and the inverse spectral problems for the equation. Guseynov used a procedure of the Gelfand-Levitan type for the case N = 1. We use another procedure and this procedure is more easy and transparent.
Direct iterative methods for linear systems using weak splittings
Direct methods for matrix Sylvester and Lyapunov equations.
Direct summands of systems of continuous linear transformations [Book]
Directed forests with application to algorithms related to Markov chains
This paper is devoted to computational problems related to Markov chains (MC) on a finite state space. We present formulas and bounds for characteristics of MCs using directed forest expansions given by the Matrix Tree Theorem. These results are applied to analysis of direct methods for solving systems of linear equations, aggregation algorithms for nearly completely decomposable MCs and the Markov chain Monte Carlo procedures.
Directed graphs and matrix equations
Discrete linear regulator revisited
Discrete-time symmetric polynomial equations with complex coefficients
Discrete-time symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case. New theoretical results are derived and several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically the equations. The algorithms are implemented in the Polynomial Toolbox for Matlab.
Discriminant algebras and adjoints of quadratic forms.
Displacement Structure of Generalized Inverse At,s(1,2)
Dissident algebras
Given a euclidean vector space V = (V,〈〉) and a linear map η: V ∧ V → V, the anti-commutative algebra (V,η) is called dissident in case η(v ∧ w) ∉ ℝv ⊕ ℝw for each pair of non-proportional vectors (v,w) ∈ . For any dissident algebra (V,η) and any linear form ξ: V ∧ V → ℝ, the vector space ℝ × V, endowed with the multiplication (α,v)(β,w) = (αβ -〈v,w〉+ ξ(v ∧ w), αw + βv + η(v ∧ w)), is a quadratic division algebra. Up to isomorphism, each real quadratic division algebra arises in this way. Vector...
Dissident maps on the seven-dimensional Euclidean space
Our article contributes to the classification of dissident maps on ℝ ⁷, which in turn contributes to the classification of 8-dimensional real division algebras. We study two large classes of dissident maps on ℝ ⁷. The first class is formed by all composed dissident maps, obtained from a vector product on ℝ ⁷ by composition with a definite endomorphism. The second class is formed by all doubled dissident maps, obtained as the purely imaginary parts of the structures of those 8-dimensional...
Distances on the tropical line determined by two points
Let and be points in . Write if is a multiple of . Two different points and in uniquely determine a tropical line passing through them and stable under small perturbations. This line is a balanced unrooted semi-labeled tree on leaves. It is also a metric graph. If some representatives and of and are the first and second columns of some real normal idempotent order matrix , we prove that the tree is described by a matrix , easily obtained from . We also prove that...
Distribution of values of permanent and standard forms of (0,1)-matrices