Sökning: "Quadratic forms"

Visar resultat 1 - 5 av 8 uppsatser innehållade orden Quadratic forms.

  1. 1. Octonion Algebras over Schemes and the Equivalence of Isotopes and Isometric Quadratic Forms

    Master-uppsats, Uppsala universitet/Matematiska institutionen

    Författare :Victor Hildebrandsson; [2023]
    Nyckelord :Algebraic geometry; octonion algebras;

    Sammanfattning : Octonion algebras are certain algebras with a multiplicative quadratic form. In 2019, Alsaody and Gille showed that, for octonion algebras over unital commutative rings, there is an equivalence between isotopes and isometric quadratic forms. LÄS MER

  3. 2. Three Perspectives of Schiemann’s Theorem

    Master-uppsats, Göteborgs universitet/Institutionen för matematiska vetenskaper

    Författare :Felix Rydell; [2020-06-23]
    Nyckelord :Lattice theory; Minkowski reduction; flat torus; isospectrality; spectral determination; positive definite quadratic forms; Alexander Schiemann.;

    Sammanfattning : Interest in the field of spectral geometry, the study of how analytic and geometric properties of manifolds are related, was sparked when Marc Kac in 1966 asked the question “can one hear the shape of a drum?”. One of the problems that garnered attention because of this was whether the Laplace spectrum of a flat torus determines its shape, even though it was not new. LÄS MER

  4. 3. Klassgruppen Introduktion, faktorisering och implementation

    Kandidat-uppsats, KTH/Skolan för teknikvetenskap (SCI)

    Författare :Isak Ohlsson Ångnell; [2019]
    Nyckelord :;

    Sammanfattning : Givet ett heltal n så utforskar denna text olika sätt att hitta ns faktorer, med fokus på Shanks Klassgruppmetod, även om korta beskrivningar av Pollards p -1- och rho-algoritmer ges. Klassgruppen introduceras som en mängd av ekvivalensklasser av fraktionsideal i imaginära kvadratiska talkroppar, varpå en isomorfi till en mängd av ekvivalensklasser av binära kvadratiska former av given diskriminant D ges. LÄS MER

  5. 4. Counting Class Numbers

    Master-uppsats, KTH/Matematik (Avd.)

    Författare :Tobias Magnusson; [2018]
    Nyckelord :;

    Sammanfattning : The following thesis contains an extensive account of the theory of class groups. First the form class group is introduced through equivalence classes of certain integral binary quadratic forms with a given discriminant. The sets of classes is then turned into a group through an operation referred to as "composition''. LÄS MER

  7. 5. Approximating extrema of quadratic forms using Krylov subspaces

    Kandidat-uppsats, Lunds universitet/Matematik LTH

    Författare :Simon Hallborn; [2017]
    Nyckelord :Approximations; Quadratic forms; Krylov subspaces; Eigenvalue problems; Norms; Logarithmic norms; Mathematics and Statistics;

    Sammanfattning : In this thesis approximations to quadratic forms using Krylov subspaces are presented. These quantities are approximations of the norm and logarithmic norm of a matrix. In order to find these quantities an eigenvalue problem has to be solved, but because of limited storage and time, this is not feasible in practice with large matrices. LÄS MER