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...
Non-trivial solutions to certain matrix equations.
Norm attaining bilinear forms on C*-algebras
We give a sufficient condition on a C*-algebra to ensure that every weakly compact operator into an arbitrary Banach space can be approximated by norm attaining operators and that every continuous bilinear form can be approximated by norm attaining bilinear forms. Moreover we prove that the class of C*-algebras satisfying this condition includes the group C*-algebras of compact groups.
Norm Bounds for Rational Matrix Functions.
Norm estimates for functions of two commuting matrices.
Norm estimates for functions of two non-commuting matrices.
Norm Estimates for Inverses of Vandermonde Matrices.
Norm estimates for solutions of matrix equations AX-XB=C and X-AXB=C
Let A, B and C be matrices. We consider the matrix equations Y-AYB=C and AX-XB=C. Sharp norm estimates for solutions of these equations are derived. By these estimates a bound for the distance between invariant subspaces of matrices is obtained.
Norm estimates for the inverses of matrices of monotone type and totally positive matrices.
Normal forms of matrices in topoi
Normal matrix polynomials with nonsingular leading coefficients.
Norms and Determinants of Linear Mappings.
Norms of certain rational functions of a matrix and Schur's criterion for polynomials
Norms of matrix powers