Equations fonctionnelles et estimations de normes de matrices.
Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics
We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.
Equivalence and congruence of matrices under the action of standard parabolic subgroups.
Equivalence of von Neumann regular and idempotent matrices
Errata to the paper: Craig M. Cordes, Kaplansky's radical and quadratic forms over non real fields (pp. 251-261)
Erratum: "Embeddings of 2-spheres in 4-manifolds".
Erratum. Factorization Iterative Methods, M-operators and H-Operators. (Num. Math. 31, 335-357 (1979)).
Erratum: “Lower bounds for some factorable matrices" [Int. J. Math. Math. Sci. 2006, No. 14, Article ID 76135 (2006; Zbl pre05231649)].
Erratum to "Algebraic and topological properties of some sets in ℓ₁" (Colloq. Math. 129 (2012), 75-85)
Erratum to On feebly nil-clean rings
Espacios de producto interno (II).
Among normal linear spaces, the inner product spaces (i.p.s.) are particularly interesting. Many characterizations of i.p.s. among linear spaces are known using various functional equations. Three functional equations characterizations of i.p.s. are based on the Frchet condition, the Jordan and von Neumann identity and the Ptolemaic inequality respectively. The object of this paper is to solve generalizations of these functional equations.
Essential decomposition of polynomially normal matrices in real indefinite inner product spaces.
Essential sign change numbers of full sign pattern matrices
A sign pattern (matrix) is a matrix whose entries are from the set {+, −, 0} and a sign vector is a vector whose entries are from the set {+, −, 0}. A sign pattern or sign vector is full if it does not contain any zero entries. The minimum rank of a sign pattern matrix A is the minimum of the ranks of the real matrices whose entries have signs equal to the corresponding entries of A. The notions of essential row sign change number and essential column sign change number are introduced for full sign...
Essentially Hermitian matrices revisited.
Estimates for absolute values of matrix functions.
Estimates of determinants and of the elements of the inverse matrix under conditions of Ostrovskii theorem.
Estimating the matrix p-norm.
Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix.
Estimation of the noncentrality matrix of a noncentral Wishart distribution with unit scale matrix. A matrix generalization of Leung's domination result.
The main aim is to estimate the noncentrality matrix of a noncentral Wishart distribution. The method used is Leung's but generalized to a matrix loss function. Parallelly Leung's scalar noncentral Wishart identity is generalized to become a matrix identity. The concept of Löwner partial ordering of symmetric matrices is used.
Étienne Bézout : analyse algébrique au siècle des lumières
Le but de cet article, à travers l’étude des travaux en analyse algébrique finie d’Étienne Bézout (1730-1783), est de mieux faire connaître ses résultats, tels qu’il les a effectivement trouvés, et de mettre en valeur aussi bien les points de vue novateurs que les méthodes originales, mis en œuvre à cet effet. L’idée de ramener le problème de l’élimination d’une ou plusieurs inconnues à l’étude d’un système d’équations du premier degré, son utilisation inhabituelle des coefficients indéterminés...