Ein Teilformensatz für quadratische Formen in Charakteristik 2.
Eine axiomatische Kennzeichnung der Determinante auf endlich-erzeugten, projektiven Moduln.
Eine Begründung der Resultantentheorie durch einen elementaren Beweis der Cayieysdaen Konstruktion
Eine Bemerkung zu dichten Unterräumen reeller quadratischer Räume.
Eine Charakterisierung der positiv definiten quadratischen Formen.
Eine Charakterisierung quadratischer Formen durch eine Funktionengleichung. (Short Communication).
Eine Charakterisierung quadratischer Formen durch eine Funktionengleichung.
Eine Eigenwertabschätzung für Integraloperatoren mit stochastischen Kernen
Eine Faktorisierung der bei der rationalen Interpolation auftretenden Matrizen.
Eine homologische Interpretation gewisser Inzidenzmatrizen mod p.
Eine Untersuchung zur Auflösung magerer Gleichungssysteme.
Einige Bemerkungen über eine Determinante.
Einige Eigenschaften monotoner Matrizen.
Elementary linear algebra for advanced spectral problems
We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators of mathematical...
Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices
We use elementary triangular matrices to obtain some factorization, multiplication, and inversion properties of triangular matrices. We also obtain explicit expressions for the inverses of strict k-Hessenberg matrices and banded matrices. Our results can be extended to the cases of block triangular and block Hessenberg matrices. An n × n lower triangular matrix is called elementary if it is of the form I + C, where I is the identity matrix and C is lower triangular and has all of its nonzero entries...
Éléments de probabilités quantiques. XI. Caractérisation des lois de Bernoulli quantiques d'après K. R. Parthasarathy
Elimination on sparse symmetric systems of a special structure
Embedded Lattice and Properties of Gram Matrix
In this article, we formalize in Mizar [14] the definition of embedding of lattice and its properties. We formally define an inner product on an embedded module. We also formalize properties of Gram matrix. We formally prove that an inverse of Gram matrix for a rational lattice exists. Lattice of Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm [16] and cryptographic systems with lattice [17].
Embedding properties of endomorphism semigroups
Denote by PSelf Ω (resp., Self Ω) the partial (resp., full) transformation monoid over a set Ω, and by Sub V (resp., End V) the collection of all subspaces (resp., endomorphisms) of a vector space V. We prove various results that imply the following: (1) If card Ω ≥ 2, then Self Ω has a semigroup embedding into the dual of Self Γ iff . In particular, if Ω has at least two elements, then there exists no semigroup embedding from Self Ω into the dual of PSelf Ω. (2) If V is infinite-dimensional, then...
Embeddings of 2-spheres in 4-manifolds.