A 1-norm bound for inverses of triangular matrices with monotone entries.
A class of inverse -matrices.
A Fiedler-like theory for the perturbed Laplacian
The perturbed Laplacian matrix of a graph is defined as , where is any diagonal matrix and is a weighted adjacency matrix of . We develop a Fiedler-like theory for this matrix, leading to results that are of the same type as those obtained with the algebraic connectivity of a graph. We show a monotonicity theorem for the harmonic eigenfunction corresponding to the second smallest eigenvalue of the perturbed Laplacian matrix over the points of articulation of a graph. Furthermore, we use...
A matrix-polynomial structure in a finite-dimensional vector space.
A new decomposition for square matrices.
A new look at totally positive matrices
A close relationship between the class of totally positive matrices and anti-Monge matrices is used for suggesting a new direction for investigating totally positive matrices. Some questions are posed and a partial answer in the case of Vandermonde-like matrices is given.
A new series of conjectures and open questions in optimization and matrix analysis
We present below a new series of conjectures and open problems in the fields of (global) Optimization and Matrix analysis, in the same spirit as our recently published paper [J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review 49 (2007) 255–273]. With each problem come a succinct presentation, a list of specific references, and a view on the state of the art of the subject.
A new series of conjectures and open questions in optimization and matrix analysis
We present below a new series of conjectures and open problems in the fields of (global) Optimization and Matrix analysis, in the same spirit as our recently published paper [J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review49 (2007) 255–273]. With each problem come a succinct presentation, a list of specific references, and a view on the state of the art of the subject.
A Note on Chessboard Matrices
A note on involutory automorphisms of and the use of algebraically independent numbers for the construction of diagonable matrices
A note on Kantorovich inequality for Hermite matrices.
A note on symetric matrices
A note on symplectic block reflectors.
A note on the convexity of the realizable set of eigenvalues for nonnegative symmetric matrices.
A note on the spectra of tridiagonal matrices.
A note on the trace inequality for products of Hermitian matrix power.
A note on ultrametric matrices
It is proved in this paper that special generalized ultrametric and special matrices are, in a sense, extremal matrices in the boundary of the set of generalized ultrametric and matrices, respectively. Moreover, we present a new class of inverse -matrices which generalizes the class of matrices.
A remark on confluent Cauchy and confluent Loewner matrices
A simple cocyclic Jacket matrices.
A simple proof of the classification of normal Toeplitz matrices.