MATRICES OF LINEAR OPERATORS

Abstract

The classical Hamilton-Cayley theorem is extended as follows to matrices of operators on a Banach space B. Let = a sub ij I + K sub ij , i,j = 1,..., m, where the a sub ij are scalars, I is the identity operator on B, and the K sub ij are compact linear operators on B. Let P(lambda) be the characteristic polynomial of a sub ij . Then P( ) represents a compact operator on the product space B-m. This theorem is applied to the study of the asymptotic behavior of a sequence of elements in B which satisfy a composite recusion formula. In addition, the theorem is generalized to an abstract algebraic setting. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1962
Accession Number
AD0292918

Entities

People

  • P.m. Anselone

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Banach Space
  • Composite Materials
  • Identities
  • Mathematics
  • Polynomials
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Linear Algebra

Technology Areas

  • Space