Computability in linear algebra

  • Authors:
  • Martin Ziegler;Vasco Brattka

  • Affiliations:
  • Computer Science Department, Heinz Nixdorf Institute, University of Paderborn, 33095 Paderborn, Germany;Department of Mathematics & Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2004

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Abstract

Many problems in Linear Algebra can be solved by Gaussian Elimination. This famous algorithm applies to an algebraic model of real number computation where operations +, -, *, / and tests like, e.g., A ċ x = b, • determine the spectral resolution of a symmetric matrix B, • and compute a linear subspace's dimension from its Euclidean distance function, provided the rank of A and the number of distinct eigenvalues of B are known. Without such restrictions, the first two problems are shown to be, in general, uncomputable.