On symmetric matrices with indeterminate leading diagonals

  • A. V. Seliverstov
  • V. A. Lyubetsky
Large Systems


We consider properties of the matrix of a real quadratic form that takes a constant value on a sufficiently large set of vertices of a multidimensional cube centered at the origin given that the corresponding quadric does not separate vertices of the cube. In particular, we show that the number of connected components of the graph of the matrix of such a quadratic form does not change when one edge of the graph is deleted.


  1. 1.
    Fallat, S.M. and Hogben, L., The Minimum Rank of Symmetric Matrices Described by a Graph: A Survey, Linear Algebra Appl., 2007, vol. 426, no. 2–3, pp. 558–582.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Fiedler, M., A Characterization of Tridiagonal Matrices, Linear Algebra Appl., 1969, vol. 2, no. 2, pp. 191–197.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bento, A. and Leal Duarte, A., On Fiedler’s Characterization of Tridiagonal Matrices over Arbitrary Fields, Linear Algebra Appl., 2005, vol. 401, pp. 467–481.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Schrijver, A., Theory of Linear and Integer Programming, Chichester: Wiley, 1986. Translated under the title Teoriya lineinogo i tselochislennogo programmirovaniya, Moscow: Mir, 1991.zbMATHGoogle Scholar
  5. 5.
    Harris, J., Algebraic Geometry: A First Course, New York: Springer, 1995, 3rd ed. Translated under the title Algebraicheskaya geometriya. Nachal’nyi kurs, Moscow: MCCME, 2005.Google Scholar
  6. 6.
    Hartshorne, R., Algebraic Geometry, New York: Springer, 1977. Translated under the title Algebraicheskaya geometriya, Moscow: Mir, 1981.zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Kharkevich Institute for Information Transmission ProblemsRASMoscowRussia

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