Journal: Linear Algebra and its Applications

Abbreviation

Linear Algebra Appl.

Publisher

Elsevier

Journal Volumes

ISSN

0024-3795
1873-1856

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Publications 1 - 10 of 20
  • A case when the union of polytopes is convex
    Item type: Journal Article
    Bárány, Imre; Fukuda, Komei (2005)
    Linear Algebra and its Applications
    We present a necessary and sufficient condition for the union of a finite number of convex polytopes in ℝd to be convex. This generalises two theorems on convexity of the union of convex polytopes due to Bemporad et al.
  • On varieties of commuting nilpotent matrices
    Item type: Journal Article
    Ngo, Nham V.; Šivic, Klemen (2014)
    Linear Algebra and its Applications
  • Exotic one-parameter semigroups of endomorphisms of a symmetric cone
    Item type: Journal Article
    Kuzma, Bojan; Omladič, Matjaž; Šivic, Klemen; et al. (2015)
    Linear Algebra and its Applications
  • Cluster tilting modules for mesh algebras
    Item type: Journal Article
    Erdmann, Karin; Gratz, Sira; Lamberti, Lisa (2021)
    Linear Algebra and its Applications
    We study cluster tilting modules in mesh algebras of Dynkin type as defined in [12], providing a new proof for their existence. Except for type G2, we show that these are precisely the maximal rigid modules, and that they are equivariant for a certain automorphism. We further study their mutation, providing an example of mutation in an abelian category which is not stably 2-Calabi-Yau, and explicitly describe the combinatorics.
  • Equiangular tight frames from Paley tournaments
    Item type: Journal Article
    Renes, Joseph M. (2007)
    Linear Algebra and its Applications
    We prove the existence of equiangular tight frames having n = 2 d - 1 elements drawn from either Cd or Cd - 1 whenever n is either 2k - 1 for k ∈ N, or a power of a prime such that n ≡ 3 mod 4. We also find a simple explicit expression for the prime power case by establishing a connection to a 2 d-element equiangular tight frame based on quadratic residues. © 2007 Elsevier Inc. All rights reserved.
  • Sets and multisets of range uniqueness for polynomials
    Item type: Journal Article
    Halbeisen, Lorenz; Hungerbühler, Norbert; Schumacher, Salome (2020)
    Linear Algebra and its Applications
  • Generalizing block LU factorization: A lower–upper–lower block triangular decomposition with minimal off-diagonal ranks
    Item type: Journal Article
    Serre, François; Püschel, Markus (2016)
    Linear Algebra and its Applications
  • False-twin-free graphs with a fixed number of negative eigenvalues
    Item type: Journal Article
    Basso, Giuliano (2021)
    Linear Algebra and its Applications
    We prove a quantitative version of a result of Torgašev concerning graphs with a fixed number of negative eigenvalues. We also establish a structural result stating that if for a hereditary family of graphs every graph of order N + 1 and N + 2 has false twins, then every graph from this family of order greater than N has false twins.
  • Structured eigenvalue condition numbers and linearizations for matrix polynomials
    Item type: Journal Article
    Adhikari, Bibhas; Alam, Rafikul; Kressner, Daniel (2011)
    Linear Algebra and its Applications
  • Flattening rank and its combinatorial applications
    Item type: Journal Article
    Munhá Correia, David; Sudakov, Benny; Tomon, István (2021)
    Linear Algebra and its Applications
    Given a d-dimensional tensor T:A ×…×A →F (where F is a field), the i-flattening rank of T is the rank of the matrix whose rows are indexed by A , columns are indexed by B =A ×…×A ×A ×…×A and whose entries are given by the corresponding values of T. The max-flattening rank of T is defined as mfrank(T)=max frank (T). A tensor T:A →F is called semi-diagonal, if T(a,…,a)≠0 for every a∈A, and T(a ,…,a )=0 for every a ,…,a ∈A that are all distinct. In this paper we prove that if T:A →F is semi-diagonal, then mfrank(T)≥[Formula presented], and this bound is the best possible. We give several applications of this result, including a generalization of the celebrated Frankl-Wilson theorem on forbidden intersections. Also, addressing a conjecture of Aharoni and Berger, we show that if the edges of an r-uniform multi-hypergraph H are colored with z colors such that each color class is a matching of size t, then H contains a rainbow matching of size t provided z>(t−1)(rtr). This improves previous results of Alon and Glebov, Sudakov, and Szabó.
Publications 1 - 10 of 20