• Topological solution of algebraic eigenvalue problem

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/jcsc/102/01/0051-0064

    • Keywords

       

      Undirected graph; binary operator; characteristic polynomial; eigenvalues; eigenfunctions

    • Abstract

       

      A simple graph theoretical algorithm for simultaneous determination of eigenfunctions, eigenvalues and characteristic polynomials of real symmetric matrices has been developed. The method starts with representing the matrixA−λI, whereI is an unit matrix of the size ofA, by an undirected weighted graph (G) and an assumed set of eigenfunctions. Conditions necessary to disconnect one vertex completely fromG are then developed. The method does not require any property related to the geometrical symmetry group of the graph and is applicable even to matrices containing a number of multiple eigenvalues.

    • Author Affiliations

       

      Kali Kinkar Datta1

      1. Department of Chemistry, Burdwan Raj College, Burdwan - 713 104, India
    • Dates

       
  • Journal of Chemical Sciences | News

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