A linear assignment formulation of the multiattribute decision problem
A linear programming based analysis of the CP-rank of completely positive matrices
A real matrix A is said to be completely positive (CP) if it can be decomposed as A = BB^T, where the real matrix B has exclusively non-negative entries. Let k be the rank of A and Φ_k the least possible number of columns of the matrix B, the so-called completely positive rank (cp-rank) of A. The present work is devoted to a study of a general upper bound for the cp-rank of an arbitrary completely positive matrix A and its dependence on the ordinary rank k. This general upper bound of the cp-rank...
A linearization of Connes' embedding problem.
A Markov approach to the generalized Syracuse algorithm
A matrix inequality for Möbius functions.
A matrix paraphrase of cyclotomy
A matrix representation of the Bercovici-Pata bijection.
A matrix-polynomial structure in a finite-dimensional vector space.
A Minimaximin Formula and its Application to Doubly Stochastic Matrices
A new approach to multiple class pattern classification with random matrices.
A new approach to some problems in the theory of non-negative matrices
A new decomposition for square matrices.
A new inclusion interval for the real eigenvalues of real matrices
By properties of Cvetković-Kostić-Varga-type (or, for short, CKV-type) B-matrices, a new class of nonsingular matrices called CKV-type -matrices is given, and a new inclusion interval of the real eigenvalues of real matrices is presented. It is shown that the new inclusion interval is sharper than those provided by J. M. Peña (2003), and by H. B. Li et al. (2007). We also propose a direct algorithm for computing the new inclusion interval. Numerical examples are included to illustrate the effectiveness...
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 proof of Löwner's theorem on monotone matrix functions.
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 solvable condition for a pair of generalized Sylvester equations.
A note of equivalence classes of matrices over a finite field.
A note on algorithms for determining the copositivity of a given symmetric matrix.