Essays about: "matrix algebra"

Showing result 1 - 5 of 19 essays containing the words matrix algebra.

  1. 1. Examples of G-Hom-Associative Algebras

    University essay from Mälardalens universitet/Akademin för utbildning, kultur och kommunikation

    Author : Felicia Modin; [2024]
    Keywords : G-hom-associative algebra; hom-associative algebra; hom-Lie admissible algebra;

    Abstract : In this thesis we look at hom-associative algebras (which turn out to be exactly the G1-hom-associative algebras), by, in two and three dimensions, trying to find the structure constants for which an algebra becomes hom-associative when the homomorphism 𝛼 is defined as different matrix units. These algebras are also hom-Lie admissible (or G6-hom-associative, which turn out to be the same thing) with a commutator, so we also find the commutator for each of these hom-Lie admissible algebras. READ MORE

  3. 2. Randomized Diagonal Estimation

    University essay from KTH/Matematik (Avd.)

    Author : Niclas Joshua Popp; [2023]
    Keywords : Diagonal estimation; randomized numerical linear algebra; low-rank approximation; matrix functions; Diagonalestimering; randomiserad numerisk linjär algebra; lågrankad approximation; matrisfunktioner;

    Abstract : Implicit diagonal estimation is a long-standing problem that is concerned with approximating the diagonal of a matrix that can only be accessed through matrix-vector products. It is of interest in various fields of application, such as network science, material science and machine learning. READ MORE

  4. 3. Methods from Linear Algebra for the Enumeration of Spanning Trees

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Nils Forsgren; [2023]
    Keywords : Spanning Tree Enumeration;

    Abstract : In this report, we study the enumeration of spanning trees in graphs, using two methods withinlinear algebra, Kirchhoff’s Matrix Tree Theorem and an alternative method, also referred to asLemma 1, derived by S. Klee and M.T Stamps in [KS20]. READ MORE

  5. 4. Tensor rank and support rank in the context of algebraic complexity theory

    University essay from KTH/Matematik (Avd.)

    Author : Pelle Andersson; [2023]
    Keywords : linear algebra; tensor product; tensor rank; matrix multiplication; complexity; linjär algebra; tensorprodukt; tensorrang; matrismultiplikation; komplexitet;

    Abstract : Starting with the work of Volker Strassen, algorithms for matrix multiplication have been developed which are time complexity-wise more efficient than the standard algorithm from the definition of multiplication. The general method of the developments has been viewing the bilinear mapping that matrix multiplication is as a three-dimensional tensor, where there is an exact correspondence between time complexity of the multiplication algorithm and tensor rank. READ MORE

  6. 5. Perron-Frobenius' Theory and Applications

    University essay from Linköpings universitet/Algebra, geometri och diskret matematik; Linköpings universitet/Tekniska fakulteten

    Author : Karl Eriksson; [2023]
    Keywords : Positive matrices; nonnegative matrices; Perron-Frobenius; linear dynamical systems; Leslie matrices; Markov chain; Google s PageRank algorithm; Positiva matriser; icke-negativa matriser; Perron-Frobenius; linjära dynamiska system; Leslie matris; Markov-kedja; Google s PageRank algoritm;

    Abstract : This is a literature study, in linear algebra, about positive and nonnegative matrices and their special properties. We say that a matrix or a vector is positive/nonnegative if all of its entries are positive/nonnegative. First, we study some generalities and become acquainted with two types of nonnegative matrices; irreducible and reducible. READ MORE