A matrix pencil approach for the solution of linear systems with rectangular or singular coefficient matrices

  • Authors:

  • Athanasios D. Karageorgos;Athanasios A. Pantelous;Grigoris I. Kalogeropoulos

  • Affiliations:

  • Department of Mathematics, University of Athens, Greece;Department of Mathematics, University of Athens, Greece;Department of Mathematics, University of Athens, Greece

  • Venue:
  • Neural, Parallel & Scientific Computations
  • Year:
  • 2009

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Abstract

We describe a new approach for the classical problem of solving ordinary systems of linear equations with rectangular (or singular) coefficient matrices. Using the complex Kronecker canonical form, the solution is analytically derived. This approach succeeds in decreasing the importance of arbitrary-unknown elements. Moreover, we have identified the necessary and required mathematical condition in order to be able to obtain the solutions of the subject system.