A new proof of Löwner's theorem on monotone matrix functions.
A new proof of the Millinen-Akdeniz theorem.
A simple proof is given for a theorem by Milliken and Akdeniz (1977) about the difference of the Moore-Penrose inverses of two positive semi-definite matrices.
A new rank formula for idempotent matrices with applications
It is shown that where is idempotent, has full row rank and . Some applications of the rank formula to generalized inverses of matrices are also presented.
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 new simple approach to linear dependence
A new solvable condition for a pair of generalized Sylvester equations.
A new upper bound for the eigenvalues of the continuous algebraic Riccati equation.
A new upper bound for the Laplacian spectral radius of a graph.
A Newton Iteration Process for Inverse Eigenvalue Problems.
A note of equivalence classes of matrices over a finite field.
A note on a class of homeomorphisms between Banach spaces
This paper deals with homeomorphisms F: X → Y, between Banach spaces X and Y, which are of the form where is a continuous (2n+1)-linear operator.
A note on a distance bound using eigenvalues of the normalized Laplacian matrix.
A note on Ahlers and Lewis' representation of the best linear unbiased estimator in the general Gauss-Markoff model
A note on classes of structured matrices with elliptical type numerical range
We identify new classes of structured matrices whose numerical range is of the elliptical type, that is, an elliptical disk or the convex hull of elliptical disks.
A note on computing the generalized inverse of a matrix .
A note on consecutive ones in a binary matrix.
A note on estimate of the spectral radius of symmetric matrices
A note on estimates for the spectral radius of a nonnegative matrix.
A note on estimates of diagonal elements of the inverse of diagonally dominant tridiagonal matrices.