Refined Interlacing Properties

Abstract

As for back as 1821, in the Cours d'Analyze of the Ecole Polytechnique, Augustin Cauchy published a proof of the following remarkable result. If any row, together with its matching column, is deleted from a real symmetric matrix, then the eigenvalues of the new matrix interlace the eigenvalues of the old one. In the presence of more information, much more can be said about the interlacing of eigenvalues and the relationship between the space and the corresponding eigenvectors. An example of such results can be found in a 1972 paper by G. H. Golub which discusses aspects of the Lanczos algorithm.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1991
Accession Number
ADA256584

Entities

People

  • Beresford N. Parlett
  • R. O. Hill Jr.

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Applied Mathematics
  • Computer Science
  • Eigenvalues
  • Eigenvectors
  • Inequalities
  • Interlacing
  • Intervals
  • Linear Algebra
  • Mathematics
  • Numbers
  • Numerical Analysis
  • Polynomials
  • Theorems
  • Universities

Readers

  • Linear Algebra
  • Small Business Innovation Research Program (SBIR) EDI Research and Innovation.

Technology Areas

  • Space