Non-existence of full ray nonsingular matrices.
Nonexistence results for Hadamard-like matrices.
Nonexpansive matrices with applications to solutions of linear systems by fixed point iterations.
Nonhermitian systems and pseudospectra
Four applications are outlined of pseudospectra of highly nonnormal linear operators.
Non-Homogeneous Markov Chains: Tail Idempotents, Tail Sigma-Fields and Basis.
Non-intersecting, simple, symmetric random walks and the extended Hahn kernel
We show using non-intersecting paths, that a random rhombus tiling of a hexagon, or a boxed planar partition, is described by a determinantal point process given by an extended Hahn kernel.
Nonlinear connections and spinor geometry.
Nonlinear mappings preserving at least one eigenvalue
We prove that if F is a Lipschitz map from the set of all complex n × n matrices into itself with F(0) = 0 such that given any x and y we know that F(x) - F(y) and x-y have at least one common eigenvalue, then either or for all x, for some invertible n × n matrix u. We arrive at the same conclusion by supposing F to be of class ¹ on a domain in ℳₙ containing the null matrix, instead of Lipschitz. We also prove that if F is of class ¹ on a domain containing the null matrix satisfying F(0) = 0...
Non-linear maps preserving ideals on a parabolic subalgebra of a simple algebra
Let be an arbitrary parabolic subalgebra of a simple associative -algebra. The ideals of are determined completely; Each ideal of is shown to be generated by one element; Every non-linear invertible map on that preserves ideals is described in an explicit formula.
Nonlinear maps preserving Lie products on triangular algebras
In this paper we prove that every bijection preserving Lie products from a triangular algebra onto a normal triangular algebra is additive modulo centre. As an application, we described the form of bijections preserving Lie products on nest algebras and block upper triangular matrix algebras.
Nonnegative definite hermitian matrices with increasing principal minors
A nonnegative definite hermitian m × m matrix A≠0 has increasing principal minors if det A[I] ≤ det A[J] for I⊂J, where det A[I] is the principal minor of A based on rows and columns in the set I ⊆ {1,...,m}. For m > 1 we show A has increasing principal minors if and only if A−1 exists and its diagonal entries are less or equal to 1.
Nonnegative matrices with prescribed elementary divisors.
Nonnegative realization of complex spectra.
Nonnegativity of Schur complements of nonnegative idempotent matrices.
Nonnegativity preservation under singular values perturbation.
Nonrecursive solution for the discrete algebraic Riccati equation and X + A*X -1 A=L
In this paper, we present two new algebraic algorithms for the solution of the discrete algebraic Riccati equation. The first algorithm requires the nonsingularity of the transition matrix and is based on the solution of a standard eigenvalue problem for a new symplectic matrix; the proposed algorithm computes the extreme solutions of the discrete algebraic Riccati equation. The second algorithm solves the Riccati equation without the assumption of the nonsingularity of the transition matrix; the...
Non-Replaceable Matrices.
Nonsingular unicyclic mixed graphs with at most three eigenvalues greater than two
This paper determines all nonsingular unicyclic mixed graphs on at least nine vertices with at most three Laplacian eigenvalues greater than two.
Nonsingularity and -matrices.
New proofs of two previously published theorems relating nonsingularity of interval matrices to -matrices are given.
Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding
For a real square matrix and an integer , let denote the matrix formed from by rounding off all its coefficients to decimal places. The main problem handled in this paper is the following: assuming that has some property, under what additional condition(s) can we be sure that the original matrix possesses the same property? Three properties are investigated: nonsingularity, positive definiteness, and positive invertibility. In all three cases it is shown that there exists a real number...