A new decomposition for square matrices.
A new determinant expression of the zeta function for a hypergraph.
A new equivalent condition of the reverse order law for -inverses of multiple matrix products.
A new family of companion forms of polynomial matrices.
A new family of spectrally arbitrary ray patterns
An ray pattern is called a spectrally arbitrary ray pattern if the complex matrices in give rise to all possible complex polynomials of degree . In a paper of Mei, Gao, Shao, and Wang (2014) was proved that the minimum number of nonzeros in an irreducible spectrally arbitrary ray pattern is . In this paper, we introduce a new family of spectrally arbitrary ray patterns of order with exactly nonzeros.
A new Geršgorin-type eigenvalue inclusion set.
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 a theorem about generalized orthogonal polynomials.
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.