Linear topologies on sesquilinear spaces of uncountable dimension
Linear Transformations of Euclidean Topological Spaces
We introduce linear transformations of Euclidean topological spaces given by a transformation matrix. Next, we prove selected properties and basic arithmetic operations on these linear transformations. Finally, we show that a linear transformation given by an invertible matrix is a homeomorphism.
Linear Transformations of Euclidean Topological Spaces. Part II
We prove a number of theorems concerning various notions used in the theory of continuity of barycentric coordinates.
Linear Transformations Of Tensor Spaces Preserving Decomposable Vectors
Linear transformations of tensor spaces preserving decomposable vectors.
Linear transformations on matrices: The invariance of generalized permutation matrices, II.
Linear transforms supporting circular convolution on residue class rings
Linear transforms supporting circular convolution over a commutative ring with identity
We consider a commutative ring with identity and a positive integer . We characterize all the 3-tuples of linear transforms over , having the “circular convolution” property, i.eṡuch that for all .
Lineare Abbildungen aus euklidischen Räumen
Lineare Algebra über Fastkörpern.
Lineare zweidimensionale Räume von stetigen Funktionen mit stetigen ersten Ableitungen
Linearization of Poisson actions and singular values of matrix products
We prove that the linearization functor from the category of Hamiltonian -actions with group-valued moment maps in the sense of Lu, to the category of ordinary Hamiltonian - actions, preserves products up to symplectic isomorphism. As an application, we give a new proof of the Thompson conjecture on singular values of matrix products and extend this result to the case of real matrices. We give a formula for the Liouville volume of these spaces and obtain from it a hyperbolic version of the Duflo...
Linearization of regular matrix polynomials.
Linearizations of polynomial matrices with symmetries and their applications.
Linearizations of singular matrix polynomials and the recovery of minimal indices.
Localisation de formes quadratiques. II
Localisation pour des opérateurs de Schrödinger aléatoires dans : un modèle semi-classique
Dans , nous démontrons un résultat de localisation exponentielle pour un opérateur de Schrödinger semi-classique à potentiel périodique perturbé par de petites perturbations aléatoires indépendantes identiquement distribuées placées au fond de chaque puits. Pour ce faire, on montre que notre opérateur, restreint à un intervalle d’énergie convenable, est unitairement équivalent à une matrice aléatoire infinie dont on contrôle bien les coefficients. Puis, pour ce type de matrices, on prouve un résultat...
Localization and delocalization for heavy tailed band matrices
We consider some random band matrices with band-width whose entries are independent random variables with distribution tail in . We consider the largest eigenvalues and the associated eigenvectors and prove the following phase transition. On the one hand, when , the largest eigenvalues have order , are asymptotically distributed as a Poisson process and their associated eigenvectors are essentially carried by two coordinates (this phenomenon has already been remarked for full matrices by Soshnikov...
Localization of dominant eigenpairs and planted communities by means of Frobenius inner products
We propose a new localization result for the leading eigenvalue and eigenvector of a symmetric matrix . The result exploits the Frobenius inner product between and a given rank-one landmark matrix . Different choices for may be used, depending on the problem under investigation. In particular, we show that the choice where is the all-ones matrix allows to estimate the signature of the leading eigenvector of , generalizing previous results on Perron-Frobenius properties of matrices with...
L'octogone régulier et la signature des formes quadratiques entières non singulières
La formule généralisant la loi de réciprocité quadratique de Legendre et exprimant le reste par huit de la signature d'une forme quadratique entière non dégénérée à l'aide d'une somme de Gauss est attribuée par Milnor à Milgram, la faisant remonter à Braun. Le formalisme de Witt la réduit au cas de dimension 1 que Chandrasekharan attribue à Cauchy et Kronecker. Braun soulignait que les preuves de ces formules nécessitent des moyens d'analyse. Une propriété métrique de l'octogone...