Diagonal Representation of Certain Matrices

Abstract

An explicit expression is provided for the characteristic polynomial of a matrix M of the form M = D - (0 over ba(T) ab(T) over 0), where D is a diagonal matrix, and a and b are column vectors. Also, an explicit expression is provided for the matrix of normalized eigenvectors of M, in terms of the roots of the characteristic polynomial (i.e., in terms of the eigenvalues of M).

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Document Details

Document Type
Technical Report
Publication Date
Dec 21, 2004
Accession Number
ADA458941

Entities

People

  • Mark Tygert

Organizations

  • Yale University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Computations
  • Computer Science
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Information Operations
  • Numbers
  • Observation
  • Polynomials
  • Real Numbers

Fields of Study

  • Mathematics

Readers

  • Linear Algebra