factorizations
La controverse de 1874 entre Camille Jordan et Leopold Kronecker
Une vive querelle oppose en 1874 Camille Jordan et Leopold Kronecker sur l’organisation de la théorie des formes bilinéaires, considérée comme permettant un traitement « général » et « homogène » de nombreuses questions développées dans des cadres théoriques variés au xixe siècle et dont le problème principal est reconnu comme susceptible d’être résolu par deux théorèmes énoncés indépendamment par Jordan et Weierstrass. Cette controverse, suscitée par la rencontre de deux théorèmes que nous considérerions...
L'addition parallèle d'opérateurs interprétée comme inf-convolution de formes quadratiques convexes
Laplacian integral graphs with maximum degree 3.
Large equiangular sets of lines in euclidean space.
Large structures made of nowhere functions
We say that a real-valued function f defined on a positive Borel measure space (X,μ) is nowhere q-integrable if, for each nonvoid open subset U of X, the restriction is not in . When (X,μ) has some natural properties, we show that certain sets of functions defined in X which are p-integrable for some p’s but nowhere q-integrable for some other q’s (0 < p,q < ∞) admit a variety of large linear and algebraic structures within them. The presented results answer a question of Bernal-González,...
Latent roots of lambda-matrices, Kronecker sums and matricial norms
Kronecker sums and matricial norms are used in order to give a method for determining upper bounds for where is a latent root of a lambda-matrix. In particular, upper bounds for are obtained where is a zero of a polynomial with complex coefficients. The result is compared with other known bounds for .
Latent Semantic Indexing using eigenvalue analysis for efficient information retrieval
Text retrieval using Latent Semantic Indexing (LSI) with truncated Singular Value Decomposition (SVD) has been intensively studied in recent years. However, the expensive complexity involved in computing truncated SVD constitutes a major drawback of the LSI method. In this paper, we demonstrate how matrix rank approximation can influence the effectiveness of information retrieval systems. Besides, we present an implementation of the LSI method based on an eigenvalue analysis for rank approximation...
Lattice generation program for computing a vector space lattice
Lattice of ℤ-module
In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [14], and cryptographic systems with lattices [15] and coding theory [9]....
LDU decompositions with and well conditioned.
Le nombre minimum d'invariants fondamentaux pour les formes binaires de degré 7
Le théorème fondamental des invariants pour les groupes finis
Soit un espace vectoriel complexe de dimension finie. Soit un sous-groupe fini de . On montre que pour chaque entier , le corps des fonctions rationnelles invariantes par sur s’obtient en prenant le corps des fractions de l’algèbre engendrée par les polarisées des fonctions polynômes -invariantes sur .
Least squares (P,Q)-orthogonal symmetric solutions of the matrix equation and its optimal approximation.
Left eigenvalues of symplectic matrices.
Lehrbuch der Determinanten-Theorie für Studirende [Book]
Lifting smooth homotopies of orbit spaces
Limit points for normalized Laplacian eigenvalues.
Limit points of eigenvalues of truncated unbounded tridiagonal operators
Let T be a self-adjoint tridiagonal operator in a Hilbert space H with the orthonormal basis {e n}n=1∞, σ(T) be the spectrum of T and Λ(T) be the set of all the limit points of eigenvalues of the truncated operator T N. We give sufficient conditions such that the spectrum of T is discrete and σ(T) = Λ(T) and we connect this problem with an old problem in analysis.
Line graphs: their maximum nullities and zero forcing numbers
The maximum nullity over a collection of matrices associated with a graph has been attracting the attention of numerous researchers for at least three decades. Along these lines various zero forcing parameters have been devised and utilized for bounding the maximum nullity. The maximum nullity and zero forcing number, and their positive counterparts, for general families of line graphs associated with graphs possessing a variety of specific properties are analysed. Building upon earlier work, where...